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Question: If <img src="https://cdn.pureessence.tech/canvas_411.png?top_left_x=1607&top_left_y=334&width=300&he...

If then sin⁡8θa3\frac { \sin ^ { 8 } \theta } { a ^ { 3 } } + is equal to

A

1a+b\frac { 1 } { a + b }

B

1(a+b)2\frac { 1 } { ( a + b ) ^ { 2 } }

C

1(a+b)3\frac { 1 } { ( a + b ) ^ { 3 } }

D
Answer

1(a+b)3\frac { 1 } { ( a + b ) ^ { 3 } }

Explanation

Solution

Let

then ⇒

so that

sin⁡8θa3+cos⁡8θb3=k2a4a3+k2b4b3=k2(a+b)=1(a+b)3\frac { \sin ^ { 8 } \theta } { a ^ { 3 } } + \frac { \cos ^ { 8 } \theta } { b ^ { 3 } } = \frac { k ^ { 2 } a ^ { 4 } } { a ^ { 3 } } + \frac { k ^ { 2 } b ^ { 4 } } { b ^ { 3 } } = k ^ { 2 } ( a + b ) = \frac { 1 } { ( a + b ) ^ { 3 } }