If `sintheta,tantheta,costheta` are in G.P. then `4sin^2theta-3sin^4theta+sin^6theta=_________`

Options

A. `-1`
B. 2
C. 1
D. none of these

Answer

C

Explanation

`tan^(2)theta=sin theta cos theta`
`rArr sin theta = cos^(3)theta`
Also the given expression is
`sin^(6)theta-3 sin^(4)theta + 3 sin^(2)theta -1+1+sin^(2)theta`
`=(sin^(2)theta-1)^(3)+1+sin^(2)theta`
`=-(1-sin^(2)theta)^(3)+1+sin^(2)theta`
`=-cos^(6)theta+1+sin^(2)theta`
`=-sin^(2)theta+1+sin^(2)theta=1`