Question

prove that ( sin x +cos x) ²=1+sin 2 x​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

This result follows almost directly from the following:

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

sin2(x)+cos2(x)=1

sin(2x)=2sin(x)cos(x)

With these, we have

(sin(x)+cos(x))2=sin2(x)+2sin(x)cos(x)+cos2(x)

=(sin2(x)+cos2(x))+2sin(x)cos(x)

=1+sin(2x)