Question

prove that cos(2*30°) =1-tan²30°/1+tan²30°​

Answer 1

Answer:

LHS = (2 tan 30)/(1+tan^2 30)

= (2tan30)/ (1+ sin^2 30/ cos^2 30)

= (2tan30)/ (sin^2 30 + Cos^2 30)/ cos ^2 30

= (2tan30) / (1/cos^2 30) [Because sin^2 theta + cos^2 theta =1]

= 2tan30*cos^2 30/1

= (2sin30/cos30) *cos^2 30

= 2sin 30* cos 30 [ because 2(sin theta) * (Cos theta) = sin 2 theta )

= sin 2*30

= sin60 = RHS proved. Thank you.

Answer 2

Step-by-step explanation:

Lhs = cos 60 =1/2 Rhs =(1- tan^2 30)/(1+tan^2 30) = (1- 1/3)/(1+1/3) Since tan^2 30 = 1/3 =(3-1)/(3+1) =2/4 =1/2 Lhs =Rhs