Question
If P . cos θ + Q . sin θ = 8 and P . sin θ - Q . cos
θ = 5, what is the value of (P² + Q²)?Solution
Given, P . cos θ + Q . sin θ = 8 ⇒ P² . cos² θ + Q² . sin² θ + 2PQ . sin θ . cos θ = 64  … (i) Also given, P . sin θ - Q . cos θ = 5 ⇒ P² . sin² θ + Q² . cos² θ - 2PQ . sin θ . cos θ = 25  … (ii) Adding equations (i) and (ii) P² + Q² = 89
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