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# Right-triangle relationships: Draw a right | Ch 1 - 42RE ISBN: 9780321570567 2

## Solution for problem 42RE Chapter 1

Calculus: Early Transcendentals | 1st Edition

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Problem 42RE

Right-triangle relationships: ?Draw a right triangle to simplify the given expression Ass?ume x> 0 ?and 0?????/2. csc?1? (sec ??)

Step-by-Step Solution:

Step-by-step solution Step 1 We need to draw a right triangle and use right triangle relationships to simplify 1 the expression csc (sec()) assuming x > 0 and 0 . 2 Step 2 To simplify the expression, we first draw a right triangle with an angles and , such that: 1 = csc (sec )  csc = sec We know from right triangle relationships that: hyp sec = adj and hyp csc = opp From these, we can conclude that and are complementary angles, as illustrated below: hyp C sec = adj= A csc = hyp= C opp A

Step 3 of 3

##### ISBN: 9780321570567

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