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Question
If A =30o, then prove that :
cos 2A = cos2A - sin2A = `(1 – tan^2"A")/(1+ tan^2"A")`
Sum
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Solution
Given A = 30°
cos2A = cos 2 (30°) = cos 60° = `(1)/(2)`
= `(3)/(4) – (1)/(4)`
= `(1)/(2)`
`(1 – tan^2"A")/(1 + tan^2"A") = (1 – tan^2 30°)/(1 + tan^2 30°)`
= `(1 – (1)/(3))/(1+(1)/(3)`
= `(2)/(4)`
= '(1)/(2)`
∴ cos 2A = `cos^"A" – sin^2"A" = (1 – tan^2"A")/(1 + tan^2"A")`
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