`3(sintheta-costheta)^(4)+6(sintheta+costheta)^(2)+4(sin^(6)theta+cos^(6)theta)=?`
`3(sintheta-costheta)^(4)+6(sintheta+costheta)^(2)+4(sin^(6)theta+cos^(6)theta)=?`
A. 11
B. 12
C. 13
D. 14
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Correct Answer - C
`3(sintheta-costheta)^4+6(sintheta-costheta)^2+4(sin^6theta+cos^6theta)`
`=3[sin^4theta+cos^4theta-4sin^3thetacostheta`
`+6sin^2cos^2theta-4sinthetacos^3theta]+6[1+2sinthetacostheta]`
`+4[sin^4theta+cos^4theta-sin^2thetacos^2theta]`
`=7[sin^4theta+cos^4theta]+14sin^2thetacos^2theta-12 sinthetacostheta+6+12sinthetacostheta`
`=7(sin^2theta+cos^2theta)^2+6=13`
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