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प्रश्न
f θ = 30°, verify that cos 3θ = 4 cos3 θ − 3 cos θ
उत्तर
Given:
θ = 30° ......(1)
To verify
cos 3θ = 4 cos3 θ − 3 cos θ .....(2)
Now consider left-hand side of the expression in equation (2)
Therefore
`cos 3theta = cos 3 xx 30`
= cos 90
= 0
Now consider right hand side of the expression to be verified in equation (2)
Therefore
`4cos^3 theta - 3 cos theta = 4cos^3 30 - 3 cos 30`
`= 4 xx (sqrt3/2)^3 - 3 xx (sqrt3/2)`
`= (3sqrt3)/3 = (3sqrt3)/2`
= 0
Hence it is verified that,
`cos 3theta = 4cos^3 theta - 3 cos theta`
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