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F Theta = 30°, Verify That Cos 3θ = 4 Cos3 θ − 3 Cos θ - Mathematics

f θ = 30°, verify that cos 3θ = 4 cos3 θ − 3 cos θ

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Solution

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`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 10 Trigonometric Ratios
Exercise 10.2 | Q 26.4 | Page 42
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