Question

Cos2A is equivalent to: A. sin2A−cos2A B. sin2A+cos2A C. cos2A−sin2A D. cosA−sinA

Answer 1

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

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`