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IF COS*4X/A+SIN*4/B=1/A+B SHOW THAT COS*8/A*3+SIN*8/B*3=(1/A+B)*3

IF COS*4X/A+SIN*4/B=1/A+B SHOW THAT COS*8/A*3+SIN*8/B*3=(1/A+B)*3

Grade:12th pass

2 Answers

Latika Leekha
askIITians Faculty 165 Points
5 years ago
Hello student,
We know that cos4x = (cos2x)2 = (1 – sin2x)2 = 1 + sin4x – 2sin2x
So, sin4x / b + cos4x/a = 1/(a+b)

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So, cos8x/a3 + sIn 8x/b3 = (1/a+b)3
Kushagra Madhukar
askIITians Faculty 629 Points
8 months ago
Dear student,
 
Write cosx in terms of sinx and then simplify to obtain the value of sinx
Later using this find the value of cosx
obtain both sin8x and cos8x and then substitute to get the answer
The final answer will be
cos8x/a3 + sIn 8x/b3 = 1/(a+b)3
Refer to the above answer for a more complete solution.
 
Thanks and regards,
Kushagra

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