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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`

A

`sin3A`

B

`cos3A`

C

`sinA+cosA`

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
`(sin^(3)A+sin3A)/(sinA)+(cos^(3)A-cos3A)/(cosA)`
`rArr(sin^(3)A+3sinA-4sin^(3)A)/(sinA)`
`+(cos^(3)A-[4cos^(3)A-3cosA])/(cosA)`
`rArr(3sinA-3sin^(3)A)/(sinA)+((-3cos^(3)A+3cosA))/(cosA)`
`=3-3sin^(2)A-3cos^(2)A+3`
`=6-3(cos^(2)A+sin^(2)A)=6-3(1)=3`
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NDA PREVIOUS YEARS-TRIGONOMETRY - RATIO & IDENTITY , TRIGONOMETRIC EQUATIONS-MCQ
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