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Q.
The minimum value of the function $f(x)=(3 \sin x-4 \cos x-10)(3 \sin x+4 \cos x$ $-10)$, is
Trigonometric Functions
Solution:
$f ( x )=9 \sin ^{2} x -16 \cos ^{2} x -10(3 \sin x -4 \cos x )-$
$10(3 \sin x +4 \cos x )+100$
$=25 \sin ^{2} x -60 \sin x +84$
$=(5 \sin x -6)^{2}+48$
$\therefore f ( x )_{\min }$ occurs when $\sin x =1$
minimum value $=49$