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3(sintheta-costheta)^4+6(sintheta +costh...

`3(sintheta-costheta)^4+6(sintheta +costheta)^2+4(sin^6theta+cos^6theta)` is equal to 11 (b) 12 (c) 13 (d) 14

A

11

B

12

C

13

D

14

Text Solution

Verified by Experts

The correct Answer is:
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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CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
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  11. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

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