JEE MAIN - Mathematics (2019 - 12th January Morning Slot - No. 14)
The maximum value of 3cos$$\theta $$ + 5sin $$\left( {\theta - {\pi \over 6}} \right)$$ for any real value of $$\theta $$ is :
$$\sqrt {34} $$
$$\sqrt {31} $$
$$\sqrt {19} $$
$${{\sqrt {79} } \over 2}$$
Explanation
y = 3cos$$\theta $$ + 5 $$\left( {\sin \theta {{\sqrt 3 } \over 2} - \cos \theta {1 \over 2}} \right)$$
$${{5\sqrt 3 } \over 2}$$ sin$$\theta $$ + $${1 \over 2}$$cos$$\theta $$
ymax = $$\sqrt {{{75} \over 4} + {1 \over 4}} $$ = $$\sqrt {19} $$
$${{5\sqrt 3 } \over 2}$$ sin$$\theta $$ + $${1 \over 2}$$cos$$\theta $$
ymax = $$\sqrt {{{75} \over 4} + {1 \over 4}} $$ = $$\sqrt {19} $$
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