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

Answer

1

Explanation

Given that `tan^2theta=sinthetacostheta`
`:. Sintheta=cos^3theta`
Also, given expression can be reweitten as
`sin^6theta-3sin^4theta=3sin^2theta-1+1+sin^2theta`
`=(sin^2theta-1)^3+1+sin^2theta`
`=-cos^6theta+1+sin^2theta`
`=-sin^2theta+1+sin^2theta=1`