0

Guest

Courses New

15a= 180 then solve that cosa cos2a cos3a cos4a cos5a cos6a cos7a = ??

15a= 180 then solve that cosa cos2a cos3a cos4a cos5a cos6a cos7a = ??

Grade:

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
6 years ago
562-6_Capture.PNG
Soumendu Majumdar
159 Points
6 years ago
Dear Student,
Given: 15a = 180 means a = 12
Now,
The formula required is 2cosAcosB = cos(A+B) + cos(A – B)
So
2 cos a . cos 6a = cos 7a + cos 5a
2 cos 2a . cos 7a = cos 9a + cos 5a
2 cos 3a . cos 4a = cos 7a + cos a
Now cos 5a = ½
So simplifying the equation the given equation is now like
3/4 + 1/2(cosa + 2 cos 7a + cos 9a)
Now formula required is cos C + cos D = 2 cos(C+D)/2 . cos (C – D)/2
So
3/4 + 1/2(2cos 7a + 2cos5a.cos4a)
= 3/4 + cos 7a + cos4a/2
= 3/4 + 1/2(cos2a +cosa) - sin5a(sin2a - sin a)
= 0.75 + cos 18 cos 6 – sin5a(2sin 18 sin 6)
= 0.75 + 0.95 x 0.995 – 0.866(2x0.105x0.309)
= 1.64 (approx)
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