solve...it I need...it my exam is going to start from 11 am
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Given, cos 2x cos(x/2) - cos 3x cos ( 9x/2)
On multiplying and dividing by 2 , we get
1/2 (2 cos 2x cos ( x/2) - 2 cos 3x cos ( 9x/2 ))
It is in the form of 2 cos x cos y = cos(x+y) + cos(x-y)
= 1/2 (cos(2x + x/2 ) - cos(2x - x/2 ) - cos (3x + 9x / 2 ) + cos (3x - 9x/2 ))
= 1/2 (cos 5x/2 - cos 3x/2 - cos 15x/2 + cos3x/2)
= 1/2 (cos 5x/2 - cos 15x/2)
= 1/2 (-(- 2 sin 5x sin 5x/2 ))
= sin 5x sin 5x/2
Hope this helps!
Shivam901:
check last three steps
What happened?
getting problem in last two steps how u write1/2 sin5x/2-sin15x/2 in -2sin5xsin5x/2
1/2 (cos 5x/2 - cos 15x/2)
1/2 ( -(- 2 sin 5x sin 5x/2 ))
sin 5x sin 5x/2
1/2 ( -(- 2 sin 5x sin 5x/2 ))
sin 5x sin 5x/2
cos5x/2-cos15x/2 is equal to sin5xsin5x/2 how
1/2 (-(- 2 sin 5x sin 5x/2 ))
on cancelling 2 ,we get
(-(-sin 5x sin 5x/2)
= sin 5x sin 5x/2
on cancelling 2 ,we get
(-(-sin 5x sin 5x/2)
= sin 5x sin 5x/2
There is one more solution to this problem :
= 1/2 (cos 5x/2 - cos 15x/2)
The formula is cos a- cos b= - 2 sin(a + b/2).sin(a-b/2)
= -2 sin 5x + 15x/4. sin 5x - 15x/4
= -sin 20x/4. -sin 10x/4
= sin 5x sin 5x/2
= 1/2 (cos 5x/2 - cos 15x/2)
The formula is cos a- cos b= - 2 sin(a + b/2).sin(a-b/2)
= -2 sin 5x + 15x/4. sin 5x - 15x/4
= -sin 20x/4. -sin 10x/4
= sin 5x sin 5x/2
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Answer:
Cos sin =theta log in
Thanks
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