Question

cos2A is equivalent to: A. sin2A−cos2A B. sin2A+cos2A C. cos2A−sin2A D. cosA−sinA

Answer 1

Answer:

C. $cos^2A -sin^2A$

Step-by-step explanation:

Given:

$cos2A$

To find:

The given expression is equivalent to:

A. $sin^2A-cos^2A$

B. $sin^2A+cos^2A$

C. $cos^2A -sin^2A$

D. $cosA-sinA$

Solution/Proof:

First of all, let us have a look at the compound angle formula for $cos(X+Y)$.

Compound angle means in which there is sum of two angles given.

In the above we are having X+Y i.e. sum of two angles X and Y. So it is compound angle.

The compound angle formula for cosine is given as:

$\bold{cos(X+Y)=cosXcosY-sinXsinY}$

Here, let us put X = Y = A

$cos(A+A)=cosAcosA-sinAsinA\\\Rightarrow \bold{cos(2A)=cos^2A-sin^2A}$

So, cos2A is equivalent to $cos^2A -sin^2A$.

Correct answer is:

Option C. $cos^2A -sin^2A$