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Question

If sin4Aa+cos4Ab=1a+b, then the value of sin8Aa3+cos8Ab3 is equal 5o

A
1(a+b)3
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B
a3b3(a+b)3
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C
a2b2(a+b)2
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D
None of these
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Solution

The correct option is A 1(a+b)3
sin4Aa+cos4Ab=1a+b
sin4Aa+(1sin2A)2b=1a+b
sin4Aa+1+sin4A2sin2Ab=1a+b
bsin4A+a+asin4A2asin2A=aba+b
(a+b)sin4A2asin2A+aab(a+b)=0
(a+b)2sin4A2a(a+b)sin2A+a(a+b)ab=0
[(a+b)sin2Aa]2=0
(a+b)sin2A=a
sin2A=aa+b,cos2A=ba+b
sin8Aa3+cos8Ab3=a4(a+b)4×a3+b4(a+b)4×b3=1(a+b)3
Hence, 1(a+b)3 is the correct answer.

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