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  4. If 3 sin θ+5 cos θ=5, then find the value of 5 sin θ-3 cos θ.

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Q. If $3 \sin \theta+5 \cos \theta=5$, then find the value of $5 \sin \theta-3 \cos \theta$.

Trigonometric Functions

Solution:

$9 \sin ^{2} \theta+25 \cos ^{2} \theta+30 \sin \theta \cos \theta=25$ ...(i)
$25 \sin ^{2} \theta+9 \cos ^{2} \theta-30 \sin \theta \cos \theta=x^{2}$ ...(ii)
$\Rightarrow 9+25=x^{2}+25$
$\Rightarrow x=3$