Question

(1+SinQ +CosQ) (1-CosQ+SinQ)=?
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Answer 1

Answer:

Let 1+sinQ=a and cosQ=b

(1+SinQ +CosQ) (1-CosQ+SinQ)

=(1+SinQ +CosQ) (1+SinQ-CosQ)

=(a+b)(a-b)

=a^2-b^2

=(1+SinQ)^2-(CosQ)^2

=1+2SinQ+Sin^2Q-Cos^2Q

=Sin^2Q+Cos^2Q+2SinQ+Sin^2Q-Cos^2Q

=2Sin^2Q+2SinQ

=2SinQ(SinQ+1) [Ans]

Using formula:-a^2-b^2=(a+b)(a-b)

Sin^2Q+Cos^2Q=1