(C) Given $8 \cos \theta + 15 \sin \theta = 15$. Let $x = 15 \cos \theta - 8 \sin \theta$. Consider the identity $(8 \cos \theta + 15 \sin \theta)^2 +

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(C) Given $8 \cos \theta + 15 \sin \theta = 15$. Let $x = 15 \cos \theta - 8 \sin \theta$. Consider the identity $(8 \cos \theta + 15 \sin \theta)^2 + (15 \cos \theta - 8 \sin \theta)^2 = (8^2 + 15^2)(\cos^2 \theta + \sin^2 \theta)$. Substituting the values,we get $15^2 + x^2 = (64 + 225)(1) = 289$. $225 + x^2 = 289$. $x^2 = 289 - 225 = 64$. $x = \pm 8$. Since $0 \sin \theta$. For $\theta$ in this range,$15 \cos \theta > 8 \sin \theta$,so $x$ must be positive. Therefore,$15 \cos \theta - 8 \sin \theta = 8$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Mix Examples-Trigonometrical Ratios, Functions and Identities

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If $0 < \theta < \frac{\pi}{4}$ and $8 \cos \theta + 15 \sin \theta = 15$,then $15 \cos \theta - 8 \sin \theta = $

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A
$15$
B
$7$
C
$8$
D
$23$

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If $0 < \theta < \frac{\pi}{4}$ and $8 \cos \theta + 15 \sin \theta = 15$,then $15 \cos \theta - 8 \sin \theta = $

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