Trigonometry Practice Test 2

Question : 21 of 22

Marks: +1, -0

If a sin θ + b cos θ = c, what is/are the value (s) of (a cos θ - b sin θ)?

Solution:

a sin θ + b cos θ = c

⇒(a\sinθ+b\cosθ)^2=c^2

⇒a^2\sin^2θ+b^2\cos^2θ+2ab\sinθ\cosθ=c^2

⇒a^2-a^2\cos^2θ+b^2-b^2\sin^2θ+2ab\sinθ\cosθ=c^2

⇒ a^2\cos^2θ+ b^2\sin^2θ-2ab\sinθ\cosθ=a^2+b^2-c^2

⇒(a\cosθ-b\sinθ)^2=a^2+b^2-c^2

⇒ a\cosθ-b\sinθ =±√{a^2+b^2-c^2}

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