cos theta + root under 3 sin theta =2 then find the value of theta
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Answered by
81
The answer is given below :
RULE :
sinA cosB + cosA sinB = sin(A + B)
SOLUTION :
Given,
cosθ + √3 sinθ = 2
⇒ 1/2 cosθ + √3/2 sinθ = 1
⇒ sin30° cosθ + cos30° sinθ = 1
⇒ sin(30° + θ) = sin90°
⇒ 30° + θ = 90°
⇒ θ = 90° - 30°
⇒ θ = 60°
Hence, the value of θ is 60°.
Thank you for your question.
RULE :
sinA cosB + cosA sinB = sin(A + B)
SOLUTION :
Given,
cosθ + √3 sinθ = 2
⇒ 1/2 cosθ + √3/2 sinθ = 1
⇒ sin30° cosθ + cos30° sinθ = 1
⇒ sin(30° + θ) = sin90°
⇒ 30° + θ = 90°
⇒ θ = 90° - 30°
⇒ θ = 60°
Hence, the value of θ is 60°.
Thank you for your question.
Answered by
18
Answer:cos theta - 2= -√3 sin theta
cos^2 theta - 4 cos theta +4 =3 sin^2 theta
cos^2 theta + 4 - 4 cos theta= 3 -3 cos^2 theta
4cos^2 theta - 4 cos theta + 1 =0
(2 cos theta - 1)^2=0
cos theta= 1/2
Therefore, theta = 60°
Step-by-step explanation:
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