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If Theta = 30° Verify That Sin 2theta = (2 Tan Theta)/(1 + Tan^2 Theta) - CBSE Class 10 - Mathematics

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Question

If θ = 30° verify that  `sin 2theta = (2 tan theta)/(1 + tan^2 theta)`

Solution

Given θ = 30°  ....(1)

To veriy

`sin 2theta = (2 tan theta)/(1 + tan^2 theta)` ....(2)

`sin 2 theta = sin 2 xx 30`

= sin 60

`= sqrt3/2`

Now consider right hand side

`(2 tan theta)/(1 + tan^2 theta) = (2 tan 30)/(1 + tan^2 30)`

`= (2 xx 1/sqrt3)/(1 + (1/sqrt3)^2)`

`= sqrt3/2`

Hence it is verified that,

`sin 2theta = (2 tan theta)/(1 + tan^2 theta)`

  Is there an error in this question or solution?

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Solution If Theta = 30° Verify That Sin 2theta = (2 Tan Theta)/(1 + Tan^2 Theta) Concept: Trigonometric Ratios of an Acute Angle of a Right-angled Triangle.
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