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Prove that sin^4x+cos^4x=1-2sin^2xcos^2x

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Prove that sin^4x+cos^4x=1-2sin^2xcos^2x

Posted by Ashwani Thakur 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

To prove : sin⁴x + cos⁴x = 1 - 2sin²x cos²x
We have,
LHS = sin⁴x + cos⁴x
= (sin²x)² + (cos²x)² + 2sin²x cos²x - 2 sin²x cos²x [By adding and subtracting 2sin²xcos² x]
= (sin²x + cos²x)² - 2sin²x cos²x
= 1 - 2sin²xcos²x = RHS

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CBSE > Class 10 > Mathematics