Question

Simplify the following expressions and match them with their solution.

a. sec^2x -1
b. 1/sinx
c. sinx cotx
d. sin^2x/1+cosx

Answer 1

Following are the solution to the given choices:

Explanation:

In point a:

`\to \sec^2x -1 = \tan^2 x`

In point b:

`\to (1)/(\sin x) = cosec x`

In point c:

`\to \sin x \cot x = \sin x * (\cos x)/( \sin x)\\`

`= \cos x \\`

In point d:

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

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