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

Grade:

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4405 Points
3 years ago
Soumendu Majumdar
159 Points
3 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!

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