If a cos θ + b sin θ = p and a sin θ

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If a cos θ + b sin θ = p and a sin θ –

Home » Aptitude » Trigonometry » Question

If a cos θ + b sin θ = p and a sin θ – b cos θ = q, then the relation between a, b, p and q is

1. a² – b² = p² – q²
2. a² + b² = p² + q²
3. a + b = p + q
4. a – b = p – q

Correct Option: B

a cos θ + b sin θ = p a sin θ – b cos θ = θ
On squaring and adding, a² cos² θ + b² sin² θ + 2 a b sin θ . cos θ + a² sin² θ + b² cos² θ – 2 a b sin θ. cos θ
= p² + q²
⇒ a² cos² θ + a² sin² θ + b² sin² θ + b² cos² θ = p² + q²
⇒ a² (cos²θ + sin²θ) + b² (sin²θ + cos²θ ) = p² + q²
⇒ a² + b² = p² + q²