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If sintheta+sin^(2)theta+sin^(3)theta=1,...

If `sintheta+sin^(2)theta+sin^(3)theta=1`, then find the value of `cos^(6)theta-4cos^(4)theta+8cos^(2)theta`.

A

2

B

4

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
`sin theta + sin^(2) theta + sin^(3) theta =1`
`implies sin theta + sin^(3) theta = 1 -sin^(2) theta `
`implies sin theta (1 + sin^(2) theta ) = cos^(2)theta `
` implies sin^(2) theta (1 + sin^(2) theta ) = cos^(4) theta ` [वर्ग करने पर ]
`implies (1 - cos^(2) theta ) {1 + (1- cos^(2))}^(2) = cos^(4) theta `
`implies (1 - cos^(2) theta ) {2- cos^(2)}^(2) = cos^(4) theta `
`implies (1- cos^(2) thea ) (4- 4 cos^(2) theta + cos^(4) theta ) = cos^(4) theta `
`implies 4- 4 cos^(2) theta + cos^(4) theta -4 cos^(2) theta + 4 cos^(4) theta - cos^(6) theta = cos^(4) theta `
`implies - cos^(6) theta + 4 cos^(4) theta - 8 cos^(2) theta + 4 =0`
`:. cos^(6) theta - 4 cos^(4) theta - 8 cos^(2) theta =4`
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