1) cos x*cos7x-cos5x*cos13x= A 2sin^(2)6x*cos6x B 2cos^(2)6x*cos12x C 2sin6x*cos12x D sin6x*sin12x
Answers
Given : cos x*cos7x-cos5x*cos13x
To Find : which one is Equal
A 2sin^(2)6x*cos6x
B 2cos^(2)6x*cos12x
C 2sin6x*cos12x
D sin6x*sin12x
Solution:
cos x*cos7x-cos5x*cos13x
= (1/2) [ 2 cos x*cos7x - 2cos5x*cos13x ]
2 cos A cos B = cos (A + B) + cos (A – B)
= (1/2) [ cos8x + cos(-6x) - ( cos18x + cos(-8x)]
cos (-x) = cosx
= (1/2) [ cos8x + cos( 6x) - cos18x - cos(8x)]
= (1/2) [ cos( 6x) - cos18x ]
Cos C - CosD = 2 Sin ( C + D)/2 Sin ( D - C)/2
= (1/2) 2 Sin ( 6x + 18x)/2 Sin (18x - 6x)/2
= sin 12x sin 6x
sin2A = 2SinAcosA
= 2sin6xcos6x.sin6x
= 2sin²6x cos6x
cos x*cos7x-cos5x*cos13x = 2sin²6x cos6x
Correct option is A) 2sin²6x cos6x
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