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

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{120}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{20}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

13

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\sqrt{120}$
$(5 sin x + 12 sin y)^{2} + (5 cos x + 12 cos y)^{2} = 169 + 120 cos (x - y)$
$(5 sin x + 12 sin y)^{2} + 169 = 169 + 120 cos (x - y)$
$(5 sin x + 12 sin y)^{2} = 120 cos (x - y)$
$(5 sin x + 12 sin y) = \sqrt{120 cos (x - y)}$
This is maximum when $cos (x - y)$ is maximum, which is 1 or $(x = y)$
$5 cos x + 12 cos x = 13$
$cos x = \frac{13}{17}$ which is possible.
Hence,
$5 sin x + 12 sin y = \sqrt{120}$ is the maximum value

Suggest Corrections

Similar questions

5 cos x + 12 cos y = 13

5 sin x + 12 sin y

(5 s i n x + 12 s i n y)^{2} + (5 c o s x + 12 c o s y)^{2} = 169 + 120 c o s (x - y)

5 sin x + 12 sin y

{cos}^{- 1} (\frac{3}{5} cos x + \frac{4}{5} sin x)

Find the simplified form of $c o s^{- 1} (\frac{3}{5} c o s x + \frac{4}{5} s i n x) w h e r e x \in [\frac{- 3 π}{4}, \frac{π}{4}] .$

5 sin x - 12 cos x = - 13 sin 3 x

sin ϕ = \frac{12}{13}

Join BYJU'S Learning Program