Question

If $sin^2A-cos^2A=\frac{1}{4}$, find the value of $cos^2A$.

• A. 5/8
• B. 3/8
• C. 1/2
• D. 1/4

Answer 1

Answer:

B. 3/8

Given:

$\sin^2 A - \cos^2 A = \frac14$

Use the identity:

$\sin^2 A = 1 - \cos^2 A$

Substitute:

$(1-\cos^2 A)-\cos^2 A=\frac14$
$1-2\cos^2 A=\frac14$
$2\cos^2 A = 1-\frac14$
$2\cos^2 A = \frac34$
$\cos^2 A = \frac34 \div 2$
$\cos^2 A = \frac38$

So, the value is:

$\boxed{\frac38}$