Question

prove that : sin⁴A + cos⁴A/1-2sin²Acos²A = 1​

Answer 1

Answer:

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Answer 2

Answer:

       $We \ have,\\\\To \ prove :\\\\ \frac{sin^4A + cos^4A}{1-2sin^2A\ cos^2A} =1\\\\L.H.S \\\\= \frac{(sin^2A+cos^2A)^2 -2 \ sin^2A\ cos^2A}{1 \ - \ 2 \ sin^2A \ cos^2A}\ \ \ \ \ \ \ \ \ \ [ \ a^2+b^2 = (a+b)^2-2ab\ ] \\\\= \frac{1^2 -2 \ sin^2A\ cos^2A }{1 \ - \ 2 \ sin^2A \ cos^2A}\ \ \ \ \ \ \ \ \ \ \ \ [sin^2A +cos^2A = 1]\\\\= 1 \ = R.H.S \ \ (Proved)$

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