Question

If 2sin²β – cos²β = 2, then β is​

Answer 1

Answer:

beta= 90°

Step-by-step explanation:

sin^2 beta + cos^2 beta= 1 ...(i)

2sin^2beta - cos^2beta= 2

or 2sin^2 beta= 2+ cos^2 beta = 2*1 + cos^2 beta

or 2sin^2 beta=2(sin^2 beta + cos^2 beta) +. cos^2 beta

or 2sin^2 beta= 2sin^2 beta + 3cos^2 beta

or 3cos^2 beta = 0

or √3 cos beta = 0

or cos beta= 0

according to trigonometric tables, cos 0= 90°

Answer 2

SOLUTION

TO DETERMINE

If 2sin²β – cos²β = 2 then β is

EVALUATION

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°

FINAL ANSWER

If 2sin²β – cos²β = 2 then β is 90°

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