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Prove that: (cos^(3)A-cos3A)/(cosA)+(s...

Prove that:
`(cos^(3)A-cos3A)/(cosA)+(sin^(3)A+sin3A)/(sinA)=3`

Text Solution

Verified by Experts

LHS `=(cos^(3)A-cos3A)(cosA)+(sin^(3)A+sin3A)/(sinA)`
`=cos^(3)A-(4cos^(3)A-3cosA)/(cosA)`
`=cosA(cos^(2)A-4cos^(2)A+3)/(cosA) + (sinA(sin^(2)A+3-4sin^(2)A))/(sinA)`
`=3cos^(2)A+3+3-3sin^(2)A`
`=-3(cos^(2)A+sin^(2)A)+6`
`=-3+6=3`=RHS Hence Proved.
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