help@askiitians.com

+91-735-322-1155

Trigonometry> root 2 cosx+ root6 sinx= max (sintheta + ...

question mark

root 2 cosx+ root6 sinx= max (sintheta + costheta) where theta belongs to R find the general value of x

keerthi priya , 11 Years ago

Grade 11

2 Answers

Jitender Singh

Ans:Hello student, please find answer to your question
$\sqrt{2}cosx + \sqrt{6}sinx = max(sin\theta +cos\theta )$
$f(\theta ) = \sin\theta +cos\theta$
$f'(\theta ) = cos\theta -sin\theta = 0$
$\theta = n\pi + \frac{\pi }{4}$
$[f(\theta )]_{max} = \sqrt{2}$
$\sqrt{2}cosx + \sqrt{6}sinx = \sqrt{2}$
$cosx + \sqrt{3}sinx = 1$
$\frac{1}{2}.cosx + \frac{\sqrt{3}}{2}sinx = \frac{1}{2}$
$sin(x + \frac{\pi }{6}) = sinx.\frac{\sqrt{3}}{2} + cosx.\frac{1}{2}$
$sin(x + \frac{\pi }{6}) = \frac{1}{2}$
$x + \frac{\pi }{6} = 2n\pi + \frac{\pi }{6}$
$x = 2n\pi$

Approved

Last Activity: 11 Years ago

keerthi priya

thnk u very much

Last Activity: 11 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.

trigonometry

1 Answer Available

Last Activity: 3 Years ago

Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720

trigonometry

1 Answer Available

Last Activity: 3 Years ago

To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA

trigonometry

1 Answer Available

Last Activity: 3 Years ago

Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)

trigonometry

1 Answer Available

Last Activity: 3 Years ago

WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥

trigonometry

1 Answer Available

Last Activity: 3 Years ago

View all Questions