Question

(sina+cosa)^2-(sina-cosa)^2=4sinacosa​

Answer 1

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$(sinA+cosA)^2-(sinA-cosA)^2$

Now using the identity

${x}^{2} - {y}^{2} = (x + y)(x - y)$

We get

Given Expression

$= (sinA+cosA + sinA - cosA)(sinA+cosA - sinA + cosA)$

$= 2sinA \times 2cosA$

$= 4sinA \: cosA$

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Answer 2

Step-by-step explanation:

(sina+cosa)^2-(sina-cosa)^2

now

( a+b)^2= a2 +2ab+b2

Then

sina2+2sinacosa+Cosa2 - (Sina2-2sinacosa+cosa)

=sina+2sinacosa-cos+cosa2-sina2+2Sinacosa-cosa2

=4sinacosa