Question

Which of the following options represents a logical first step that can be used

1
2
to prove the trigonometric identity
1-sin(x) '1+sin(x) cos? (x)
+
?
O
A.
1+sin(x) +1-sin(x)
1-sin(x)
2
cos? (x)
B.
1
1
1
1-sin(x) 1+sin(x)
1
2
cos(x)
C.
2
1
1-sin(x) cos(x) 1+sin(x)
D.
2
1
1+sin(x) cos'(x) 1-sin(x)

Answer 1

A)
`(1+sin(x)+1-sin(x))/(1-sin^2(x))=(2)/(cos^2(x))`

Explanation:

By combining the fractions on the left side into one fraction, we have:

`(1)/(1-sin(x))+(1)/(1+sin(x))=(2)/(cos^2(x))\\ \\(1+sin(x)+1-sin(x))/((1-sin(x))(1+sin(x)))=(2)/(cos^2(x))\\\\(1+sin(x)+1-sin(x))/(1-sin^2(x))=(2)/(cos^2(x))`

Also, given the Pythagorean Identity
`sin^2(x)+cos^2(x)=1`, then
`cos^2(x)=1-sin^2(x)`.