How am I supposed to expand \sin^2 A+\sin^4 A=1 into

Mary Reyes

Mary Reyes

Answered question

2022-01-01

How am I supposed to expand sin2A+sin4A=1 into 1+sin2A=tan2A?

Answer & Explanation

Paul Mitchell

Paul Mitchell

Beginner2022-01-02Added 40 answers

sin2A+sin4A=1
sin4A=1sin2A
sin2Asin2A=cos2A
sin2A(1cos2A)=cos2A
sin2Asin2Acos2A=cos2A
sin2A=cos2A+sin2Acos2A
sin2A=cos2A(1+sin2A)
1+sin2A=sin2Acos2A
1+sin2A=tan2A
soanooooo40

soanooooo40

Beginner2022-01-03Added 35 answers

Hint
If sin2A+sin4A=1sin4A=cos2A
Can you proceed from here?
Additional Info
sin2A(1cos2A)=cos2A
sin2A=cos2A+sin2Acos2A
Divide by cos2A
Vasquez

Vasquez

Expert2022-01-08Added 669 answers

sin2A=1sin4Asin2A=(1sin2A)(1+sin2A)sin2A=(cos2A)(1+sin2A)tan2A=1+sin2A

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