Question

Q. 2. Prove that:
(sin^4 a + cos^4 a)/
1-2 sin^2 a cos^2 a
= 1

Answer 1

Step-by-step explanation:

(sin⁴a +cos⁴a)/(1-2sin²a cos ²a)

= {(sin²a)² + (cos²a)²}/ (1-sin² a cos²a)

= {(sin²a+cos²a)²-2sin²acos²a} /(1-sin²acos²a)

[apply a²+b²= (a+b)²-2ab law)

= (1-sin²acos²a)/(1-sin²acos²a). { we know sin²a +cos²a=1}

=1(proved)