QJEEM19Ma9f07: JEE Main 2019 Mathematics - Class 11 JEEM19Ma9f07 Solution: The maximum value of 3cos θ + 5sin ( θ − π 6 ) for any real…

Question

Verified Solution • 2025–26 Session moderate

The maximum value of 3cos

θ

+ 5sin

(θ - \frac{π}{6})

for any real value of

θ

is :

Accepted Answer

y = 3cos

θ

+ 5

(\sin θ \frac{\sqrt{3}}{2} - \cos θ \frac{1}{2})

\frac{5 \sqrt{3}}{2}

sin

θ

+

\frac{1}{2}

cos

θ

y_max =

\sqrt{\frac{75}{4} + \frac{1}{4}}

=

\sqrt{19}

Step-by-Step Verified Solution