Question

prove that cos (2×30°) = 1-tan^2 30°/1+tan^2 30°​

Answer 1

Answer:

the question of proving

Step-by-step explanation:

hey

there are two ways of solving this

1)is formula method

2) solving method

let discuss both the methods

1) since cos2θ= (1-tan²θ)/(1+tan²θ)

and where θ= 30°

so

cos(2*30°) = (1-tan²30)/(1+tan²30)

and second method is

put the following values

then it will be

cos60 =(1-tan²30)/(1+tan²30)

1/2=(1-([1/√3]²)/(1+[1/√3]²)

1/2=(1-1/3)/(1+1/3)

1/2=(3-1)/(3+1)

1/2=2/4

1/2

hence proved

Answer 2

Answer:

RHS,

$\frac{1 - {tan}^{2} 30}{1 + {tan}^{2}30 } = \frac{1 - {tan}^{2}30 }{ {sec}^{2}30 } = \\ \frac{1}{ {sec}^{2}30 } - \frac{ {tan}^{2} 30}{ {sec}^{2}30 } = \\ {cos}^{2} 30 - {sin}^{2} 30 = \\ \cos(2 \times 30)$

LHS. Proved.