SSC CHSL Model Paper 20

Question : 62 of 100

Marks: +1, -0

If Pcosθ + Qsinθ = 8 and Psinθ - Qcosθ = 5, then the value of

(\P^2 + \Q^2)

Solution:

Pcosθ + Qsinθ = 8
Square the above equation:

P^2\cos^2θ + Q^2\sin^2θ

+ 2\PQ\cosθ \sinθ = 64 (1)

Psinθ - Qcosθ = 5
Square the above equation:

\P^2\sin^2θ + \Q^2\cos^2θ

- 2\PQ\sinθ \cosθ = 25 (2)

Adding (1) and (2)

(P^2 + Q^2)(\sin^2θ + \cos^2θ) = 89

P^2 + Q^2 = 89

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