SSC CPO SI and ASI Model Paper 9

Question : 126 of 200

Marks: +1, -0

Find the value of a sinθ + b cosθ, if a cosθ – b sinθ = c.

Solution:

(2) Let a sinθ + b cosθ = x
And a cosθ – b sinθ= c
On squaring and adding both theequations, we get

a^2 sin^2θ + b^2 cos^2θ+ 2absinθcosθ + a^2cos2θ + b^2sin2θ –2ab sinθcosθ = x^2 + c^2

a^2(sin^2θ + cos^2θ) + b^2(sin2θ +cos2θ) = x^2 + c^2

x^2 = a^2 + b^2 – c^2

x = ±√ {a^2 + b^2 - c^2}

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