Question

cosA^ 4 -sinA^ 4= 2cos^A-1

Answer 1

Correct Question

• Cos⁴-sin⁴=2cos²-1

AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• Cos⁴-sin⁴=2cos²-1

${\sf{\green{\underline{\large{To\:find}}}}}$

• LHS=RHS

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Cos⁴-sin⁴=2cos²-1

LHS

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Cos⁴-sin⁴

=>Cos⁴-sin⁴ breaking into a²-b²=(a+b)(a-b)

=>(cos²)²-(sin²)²

=>(cos²-sin²) (cos²+sin²).

from identity(cos²+sin²)=1

=>(cos²-sin²) 1

=> cos²-(1-cos²)

=>cos²-1+cos²

=>2cos²-1

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LHS = RHS (verified)