Question

2sin²x+sin²(2x)=2...find x​

Answer 1

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Refer attachment..

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Answer 2

It's goes like this .......

2sin^2x+ (2sinx.cosx)^2=2 

2sin^2x+4sin^2x.cos^2x=2 

sin^2x+2sin^2x.cos^2x=1 

2sin^2x.cos^2x= 1-sin^2x 

2sin^2x.cos^2x= cos^2x 

2sin^2x=1 

sin^2x= 1/2 

sinx= 1/√2 

=> x= pi/4 or 45 degrees 

Since the value of sinx repeats after every 180 deg turn, so....you would get the same value of sinx if you add pi to pi/4 or 2pi to pi/4. The solutions are countless. 

x= pi/4, 3pi/4 etc

..............hope it helps you ❤️