Help me to prove that \arcsin(\sqrt{2}\sin(t))+\arcsin(\sqrt{\cos(2t)})=\pi/2

Adrienne Rowe

Adrienne Rowe

Answered question

2022-02-28

Help me to prove that
arcsin(2sin(t))+arcsin(cos(2t))=π2

Answer & Explanation

Balraj Conrad

Balraj Conrad

Beginner2022-03-01Added 9 answers

Let
arcsin(2sint)=ysiny=2sint
cos2t=12sin2t=12(siny2)2=1sin2y=cos2y
So,
arcsincos2t=arcsin(cosy)=arcsin(sin(π2y))
Hence,
arcsincos2t=π2y=π2arcsin(2sint)

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