Question

If 2sin2β – cos2β = 2, then β is​

Answer 1

second part

0=2cos²B+cos²B

0=3cos²B

3cos²B=0

cos²B=0

cosB=0

Answer 2

If 2sin²β – cos²β = 2 then β is 90°

Given : 2sin²β – cos²β = 2

To find : The angle β

Solution :

Here it is given that

2sin²β – cos²β = 2

Now

2sin²β – cos²β = 2

⇒ 2sin²β – ( 1 - sin²β ) = 2

⇒ 2sin²β - 1 + sin²β = 2

⇒ 3sin²β - 1 = 2

⇒ 3sin²β = 3

⇒ sin²β = 1

⇒ sinβ = 1

⇒ β = 90°

Thus we have β = 90°

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