First slide

Extreme values and Periodicity of Trigonometric functions

Question

If $5 \cos x + 12 \cos y = 13,$ then the maximum value of $5 \sin x + 12 \sin y$ is

Moderate

A

12
B

$\sqrt{120}$
C

$\sqrt{20}$
D

13

Solution

Take $5 \sin x + 12 \sin y = k$ and squaring and adding the both the equations.
25+144+120cos(x-y)=169+ $k^{2}$
cos(x-y) maximum is 1 $\Rightarrow k^{2} = 120 \Rightarrow k = \sqrt{120}$

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