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Prove each of the following identities.2 - 2 cos 2x = sec

Trigonometry | ISBN: 9780495108351 | Authors: Charles P McKeague ISBN: 9780495108351 200

Solution for problem 5.1.224 Chapter 5.3

Trigonometry

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Trigonometry | ISBN: 9780495108351 | Authors: Charles P McKeague

Trigonometry

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Problem 5.1.224

Prove each of the following identities.2 - 2 cos 2x = sec x csc x - cot x + tan x sin 2x

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Islamic Education in African Societies To leave would be to capitulate (during the colonialism period); Others called for hijra; Others interpreted it as the beginning of the end  Focus on inner path—mysticism Adaptibility  Nothing is fixed; Not static  Even institutions changed over time; Islamic schools were never static (even in pre­colonial times) o Oral tradition—what gets passed down is modified and cast in a way that reflects current circumstances  Variety of strategies (e.g. mneumonic devices) o Translations into vernacular languages o Continual change after colonialism (response to secularism) Bronner and Umar  Foucault (French philosopher) o Transmission of knowledge is decided by those in power (who receives knowledge) o Dissemination of knowledge parallels with socio­economic order o Different types/levels of knowledge  Episteme: Most broadly based; Dominant way of knowing; A worldview, but not characterized by content, but by a way of producing and acquiring knowledge; Implicit; Set of norms that unite discursive practices; Inescapable  Shift from traditional to modern system during the colonial period o Pivoting from an esoteric (restricted, secretive) episteme to a “rationalistic”/democratic (open, bureaucratized) educational system  Structure becomes regularized or open, does not hinge on personal relationships anymore o Esoteric: More hierarchical; Through initiation to transform its possessor (Holistic transformation) o Rationalistic: Available to everyone; Marginalizes emotion, religion, and mysticism; Quran still accepted, but in regards of knowledge, it is openly accessible; Intellectual development not guided by spiritual development  Education separate from religious education Traditional System (Pre­colonial System)  Quran school (chuo) o Single­teachers (typically in their homes)  Students go to live with them to read and learn the Quran o “Primary school” (Graduate when fully learn Quran) o Focuses on memorizing o Memorize without comprehension o Night of the Quran o Link between memorization and devotion (piety)  Most profound act (for children); Form of respect o Cultivating a respect for the learned men and women o Bila kayf: without questioning (why/how)  God is not idol speculation o Teacher possesses Baraka (spiritual power)  Teaching is an act of piety  Majlis (‘ilm school) o Second phase; Leaving Quran school to go to another teacher(s) o Islamic disciplines based off individual texts  Usually begins with tafsir (textual interpretation/translation; learning the meaning of the Quran) Madrasa  Secular subjects taught along with religious subjects  Differences: o Critical for power and influence; critical for national development o Taught in accordance with the “rationalism”/democratic pedagogy o Primary and secondary education systems o As education is opened, opportunities for females to attend schools increases  Night classes for married women  Colonial and post­colonial periods o Waqfs: Benevolent societies o Allowed to teach Muslim subjects if also taught secular subjects  Still felt marginalized o Private Muslim schools funded by waqf funds  Inferior to the Muslim­Christian schools o Madrasas funded by mosques o Expected to meet requirements; Subsidies from government if met curriculum  1990s onward o Many funded by external donors o Influx of privatized schools  Result of economic changes  Disinvestment of public services, so they looked for foreign donors Islamic Education in African Societies To leave would be to capitulate (during the colonialism period); Others called for hijra; Others interpreted it as the beginning of the end  Focus on inner path—mysticism Adaptibility  Nothing is fixed; Not static  Even institutions changed over time; Islamic schools were never static (even in pre­colonial times) o Oral tradition—what gets passed down is modified and cast in a way that reflects current circumstances  Variety of strategies (e.g. mneumonic devices) o Translations into vernacular languages o Continual change after colonialism (response to secularism) Bronner and Umar  Foucault (French philosopher) o Transmission of knowledge is decided by those in power (who receives knowledge) o Dissemination of knowledge parallels with socio­economic order o Different types/levels of knowledge  Episteme: Most broadly based; Dominant way of knowing; A worldview, but not characterized by content, but by a way of producing and acquiring knowledge; Implicit; Set of norms that unite discursive practices; Inescapable  Shift from traditional to modern system during the colonial period o Pivoting from an esoteric (restricted, secretive) episteme to a “rationalistic”/democratic (open, bureaucratized) educational system  Structure becomes regularized or open, does not hinge on personal relationships anymore o Esoteric: More hierarchical; Through initiation to transform its possessor (Holistic transformation) o Rationalistic: Available to everyone; Marginalizes emotion, religion, and mysticism; Quran still accepted, but in regards of knowledge, it is openly accessible; Intellectual development not guided by spiritual development  Education separate from religious education Traditional System (Pre­colonial System)  Quran school (chuo) o Single­teachers (typically in their homes)  Students go to live with them to read and learn the Quran o “Primary school” (Graduate when fully learn Quran) o Focuses on memorizing o Memorize without comprehension o Night of the Quran o Link between memorization and devotion (piety)  Most profound act (for children); Form of respect o Cultivating a respect for the learned men and women o Bila kayf: without questioning (why/how)  God is not idol speculation o Teacher possesses Baraka (spiritual power)  Teaching is an act of piety  Majlis (‘ilm school) o Second phase; Leaving Quran school to go to another teacher(s) o Islamic disciplines based off individual texts  Usually begins with tafsir (textual interpretation/translation; learning the meaning of the Quran) Madrasa  Secular subjects taught along with religious subjects  Differences: o Critical for power and influence; critical for national development o Taught in accordance with the “rationalism”/democratic pedagogy o Primary and secondary education systems o As education is opened, opportunities for females to attend schools increases  Night classes for married women  Colonial and post­colonial periods o Waqfs: Benevolent societies o Allowed to teach Muslim subjects if also taught secular subjects  Still felt marginalized o Private Muslim schools funded by waqf funds  Inferior to the Muslim­Christian schools o Madrasas funded by mosques o Expected to meet requirements; Subsidies from government if met curriculum  1990s onward o Many funded by external donors o Influx of privatized schools  Result of economic changes  Disinvestment of public services, so they looked for foreign donors

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Textbook: Trigonometry
Edition:
Author: Charles P McKeague
ISBN: 9780495108351

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Prove each of the following identities.2 - 2 cos 2x = sec