Question

If 2 sin² theta - cos² theta = 2 then theta =

(a) 30°
(b) 60°
(c) 90°
(d) 45°​

Answer 1

in the given eq . we will add sin² theta and at the same time subtract sin² theta .

2 sin² theta - cos² theta = 2

+ sin theta - sin² theta

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3 sin² theta- ( cos² theta +sin² theta) = 2

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using identity cos² theta + sin² theta = 1

• 3 sin² theta - 1 = 2
• 3 sin² theta = 3
• sin² theta = 1
• sin theta = 1
• as we know the value of sin theta is 90° when sin theta = 1.
• Theta = 90°

Therefore answer is option (c) 90°

hope it helps you ..

Answer 2

Answer: sin^2 theta + cos^2 theta = 1 , sin^2 theta = 1-cos^2 theta , 2(1-cos^2 θ ) - cos ^2 θ , so 2(1-2cos^2 θ) = 2 , 2 - 4cos^2 θ = 2 , -4cos^2 θ = 0 , cos^2 θ = 0 , by taking square root of the both sides , cos θ = 0 , so angle θ = 90

Step-by-step explanation: