If 2sin2β – cos2β = 2, then β is (a) 0ᵒ (b) 90ᵒ (c) 45ᵒ (d) 30ᵒ
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12
Correct answer is: (b) 90ᵒ
2sin2β – cos2β = 2
Then 2 sin2β – (1- sin2β) = 2
3 sin2β =3 or sin2β =1
β is 90ᵒ
Answered by
3
Solution :-
→ 2sin²β – cos²β = 2
using cos²A = 1 - sin²A
→ 2sin²β - (1 - sin²β) = 2
→ 2sin²β + sin²β - 1 = 2
→ 3sin²β = 2 + 1
→ 3sin²β = 3
→ sin²β = 1
→ sinβ = ± 1
→ β = 90° , 180° .
Hence, Option (b) 90° is correct answer .
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