0

Guest

Courses New

if eight theta is equal to pi show that cos 7 theta+ cot theta is equal to zero

if eight theta is equal to pi show that cos  7 theta+ cot theta is equal to zero

Grade:11

2 Answers

Arun
25750 Points
6 years ago
8*theta=pi, so theta=pi/8.
Now, from half angle formula cos(theta/2) =± sqrt((1+ cos theta)/2).
Here pi/8 = ½ (pi/4) so we can apply half angle formula and 
get cos(pi/8) = +sqrt((1+cos pi/4)/2)
= sqrt((1+(1/sqrt 2))/2
)=sqrt((2+sqrt2)/2) –(1)
Similarly for 7pi/8, applying half angle formula.
Here 7pi/8 = ½ (7pi/4) and
cos(7pi/4)=cos(2pi-pi/4)
=cos(pi/4
)=1/sqrt(2)
So cos(7pi/8) = -sqrt((1+cos 7pi/4)/2)[negative as 7pi/8 lies in second quadrant where cos is negative] = 
-sqrt((1+(1/sqrt 2))/2)=
-sqrt((2+sqrt2)/2)—(2)
 
therefore , from (1) and (2) we get cos 7pi/4 + cos pi/4 =0
or cos 7theta + cos theta=0 (proved)
Soumendu Majumdar
159 Points
6 years ago
theta=pi/8
so cos 7theta = cos(pi-pi/8) = -cos(pi/8) =-root{(1 + cos(pi/4))/2} =-root{(2root2 + 1)/2root2}
now cos theta = cos pi/8 =root{(2root2 + 1)/2root2}
therefore cos7theta + cos theta =0
P.S--The question is wrong...it would be cos theta instead of cot theta!
Hope it helps!

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More