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Question
If 𝜃 = 30° verify `cos 2 theta = (1 - tan^2 theta)/(1 + tan^2 theta)`
Solution
Given 𝜃 = 30° ........(1)
To verify
`cos 2 theta= (1 - tan^2 theta)/(1 + tan^2 theta)` .....(2)
Now consider left hand side of the equation (2)
Therefore
`cos 2 theta = cos 2 xx 30`
= cos 60
`= 1/2`
Now consider right hand side of equation (2)
Therefore
`(1 - tan^2 theta)/(1 + tan^2 theta) = (1 - (tan 30)^2)/(1 + (tan 30)^2)`
`= (1 - (1/sqrt3)^2)/(1 + (1/2sqrt3)^2)`
`= (1 - 1/3)/(1 + 1/3)`
`= 1/2`
Hence it is verified that,
`cos 2 theta = (1 - tan^2 theta)/(1 + tan^2 theta)`
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