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Prove that : (sin3A+sin A)sin A+(cos3A-c...

Prove that : `(sin3A+sin A)sin A+(cos3A-cos A)cos A=0`

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Given,`(sin3A+sin A)sin A+(cos3A-cos A)cos A`
using, `sinA+sinB=2sin((A+B)/2)cos((A-B)/2)`
`=[2sin((3A+A)/2)cos((3A-A)/2)]sin A+[-2sin((3A+A)/2)sin((3A-A)/2)]cos A`
`=[2sin((4A)/2)cos((2A)/2)]sin A+[-2sin((4A)/2)sin((2A)/2)]cos A`
`=[2sin 2A cos A]sin A-[2sin2A sinA] cos A`
`=0`
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  2. cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

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  3. Prove that : (sin3A+sin A)sin A+(cos3A-cos A)cos A=0

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  6. Prove that 3(sinx-cosx)^4+4(sin^6x+cos^6x)+6(sinx+cosx)^2=13

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  7. cos^6A-sin^6A=cos2A(1-1/4sin^2 2A)

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  8. Prove that: tan(pi/4+theta)+tan(pi/4-theta)=2sec2theta .

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  13. If cos x=-3/5a n d\ x lies in IIInd quadrant, find the values of sin2x...

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  14. If sinx=(sqrt(5))/3a n d\ x lies in IInd quadrant, find the values of ...

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  15. Prove that 1+cos^2 2x=2(cos^4x+sin^4x)

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  16. If costheta=4/5 and theta is acute, find the tan2theta

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