Question

prove that
$sin4x + cos4x = 1 - 2 sin2x + 2sin4x$

Answer 1

Hey !!

Sin⁴x + cos⁴x

= (sin²x)² + (cos²x)²

using this identity
(a+ b)²-2ab = a² + b²

then. ( sin²x+ cos²x)² - 2sin²x ×cos²x

1 - 2sin²x×cos²x RHS prooved

Check out ur question ..
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Hope it helps you !!!

@Rajukumar111

Answer 2

heya...!!!


we know that:-


(a + b)² = a² + b² + 2ab

=> (a² + b²) = (a + b)² - 2ab---------(1)


sin⁴x + cos⁴x

=> (sin²x)² + (cos²x)²

=> (sin² + cos²)² - 2sin²xcos²x -------from(1)

=> (1)² - 2sin²x(1 - sin²x)

=> 1 - 2sin²x + 2sin⁴x