Question

If `tan A = sqrt(3)`, then find the value of cos² A – sin² А.

Answer 1

Given: `tan A = sqrt(3)`.

Step-wise calculation:

1. Use identity:

cos² A – sin² A = cos² A

2. Express cos² A in terms of tan A:

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

3. Substitute `tan A = sqrt(3)`:

`cos^2 A = (1 - 3)/(1 + 3)`

= `(-2)/4`

= `-1/2`

`cos^2 A - sin^2 A = -1/2`.