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

Answer:

Following are the solution to the given choices:

Step-by-step explanation:

In point a:

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

In point b:

$\to \frac{1}{\sin x} = cosec x$

In point c:

$\to \sin x \cot x = \sin x \times \frac{\cos x}{ \sin x}$

                    $= \cos x$

In point d:

$\to \frac{\sin^2 x}{1+ \cos x} = \frac{\sin^2 x}{1+ \cos x} \times \frac{1- \cos x}{ 1- \cos x}$

               $= \frac{\sin^2 x (1- \cos x)}{1- \cos^2 x}\\\\= \frac{\sin^2 x (1- \cos x)}{\sin^2 x}\\\\= 1-\cos x$