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If a sin θ + b cos θ = c, then a cos θ – b sin θ is equal to
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- ± √a + b - c
- ± √a² + b² + c²
- ± √a² + b² - c²
- ± √c² + a² - b²
Correct Option: C
a sinθ + b cosθ = c .... (i)
a cosθ – b sinθ = x (let) ... (ii)
On squaring equations (i) and (ii) and adding, a 2sin²θ + b 2cos²θ + 2ab sinθ. cosθ + a 2cos²θ + b 2sin²θ – 2absinθ. cosθ = c² + x²
⇒ a² (sin2θ + cos2θ) + b 2 (cos²θ + sin²θ) = c² + x²
⇒ a² + b² = c²² + x²
⇒ x² = a² + b² – c²
⇒ x = ± √a² + b² -c²
