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How do I solve this trigonometric function?

How do I solve this trigonometric function?-example-1

1 Answer

4 votes

Answer:
(1)/(cos \theta)=sec \theta

Explanation:

We have the following expression:


(1)/(2)((1+sin \theta)/(cos \theta)+(cos \theta)/(1+sin \theta))

Firstly, we have to solve what is inside the parenthesis. Let's begin by calculating the least common multiple (l.c.m), which is
cos \theta(1+sin \theta):


(1)/(2)(((1+sin \theta)^(2) +cos^(2) \theta)/(cos \theta(1+sin \theta)))


(1)/(2)((1+2sin \theta+sin^(2) \theta+cos^(2) \theta)/(cos \theta(1+sin \theta)))

Since
sin^(2) \theta+cos^(2) \theta=1:


(1)/(2)((1+2sin \theta+1)/(cos \theta(1+sin \theta)))


(1)/(2)((2(1+sin \theta))/(cos \theta(1+sin \theta)))

Simplifying:


(1)/(cos \theta)=sec \theta

User Jessann
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