Math, asked by annarosebibo, 1 month ago

if sin2beta-cos2beta=2 then beta is

Answers

Answered by MuskanJoshi14
2

Step-by-step explanation:

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Solution:

given

sin²β=sinαcosα

multiplying 2 on both sides

⇒ 2sin²β = 2sinαcosα

⇒ 1−cos2β = sin2α

⇒ cos2β = 1−sin2α→LHS

Now for cos2β=2cos²( \frac{\pi}{4}  + a)

We know

 \cos( \frac{\pi}{2} )  \:  = 0

  \sin( \frac{\pi}{2} )  = 1

Taking RHS

⇒ 2cos²( \frac{\pi}{4}  + a)

⇒ 1+cos ( \frac{2\pi}{4}  = 2a)

⇒ 1+cos ( \frac{\pi}{2}  + 2a)

⇒ 1+ ( \cos\frac{\pi}{2}  \cos2a -  \sin \frac{\pi}{2}  \sin \: a \: )

⇒ 1−sin2α

∴ LHD=RHS Proved

Answered by pulakmath007
0

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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