Question

If A =30^o, then prove that :
cos 2A = cos²A - sin²A = `(1 – tan^2"A")/(1+ tan^2"A")`

Answer 1

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")`