Trigonometry! #133

Geometry Level 1

For x ∈ [ 0 , π 2 ] x\in\left[0,\frac{\pi}{2}\right] if cos ⁡ x + cos ⁡ 2 x + cos ⁡ 3 x = 3 \cos x + \cos 2x + \cos 3x = 3 then find the value of sin ⁡ x + sin ⁡ 2 x + sin ⁡ 3 x \sin x + \sin 2x + \sin 3x

This problem is part of the set Trigonometry .


The answer is 0.

Omkar Kulkarni by Omkar Kulkarni , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Omkar Kulkarni
Feb 20, 2015

The maximum value of the cosine function is 1 1 , and hence the equality occurs only at cos ⁡ x = cos ⁡ 2 x = cos ⁡ 3 x = 1 \cos x = \cos 2x = \cos 3x = 1 , i.e. x = 0 x=0 . Hence the value of sin ⁡ x + sin ⁡ 2 x + sin ⁡ 3 x \sin x + \sin 2x + \sin 3x is 0 0 . Don't tell me you actually solved the equation. :P

2 Helpful 0 Interesting 0 Brilliant 0 Confused

:):-) its the basics What a set u have created ........ Please create a similar set for CALCULI

harsh soni - 6 years, 3 months ago

Log in to reply

I might! But as of now, I haven't learned calculus yet.

Omkar Kulkarni - 6 years, 3 months ago

Log in to reply

Ohh !!! I didn't know that....k

harsh soni - 6 years, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...