Question

(sin A + cos A)2-(sin A-cos A)2=4A cos A​

Answer 1

Appropriate Question:-

prove that :-

(Sin A + Cos A )² - (SinA - CosA)² = 4SinACosA

Solution :-

By Solving LHS :-

$\\ \quad \longrightarrow \sf {( \sin A + \cos A)}^{2} - {( \sin A - \cos A)}^{2}$

$\\ \quad \longrightarrow \sf { \sin}^{2} A + { \cos }^{2} A + 2 \sin A \cos A - ( { \sin }^{2} A + { \cos }^{2} A - 2 \sin A \cos A)$

$\\ \quad \longrightarrow \sf 1 + 2 \sin A \cos A - (1 - 2 \sin A \cos A)$

$\\ \quad \longrightarrow \sf \cancel{1} + 2 \sin A \cos A - \cancel 1 + 2 \sin A \cos A$

$\\ \quad \therefore \boxed{ \sf 4 \sin A \cos A} \bigstar$

LHS = RHS

hence Verified

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