if sin2beta-cos2beta=2 then beta is
Answers
Step-by-step explanation:
Solution:
given
sin²β=sinαcosα
multiplying 2 on both sides
⇒ 2sin²β = 2sinαcosα
⇒ 1−cos2β = sin2α
⇒ cos2β = 1−sin2α→LHS
Now for cos2β=2cos²
We know
Taking RHS
⇒ 2cos²
⇒ 1+cos
⇒ 1+cos
⇒ 1+
⇒ 1−sin2α
∴ LHD=RHS Proved
SOLUTION
CORRECT QUESTION
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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