Question

If  = 30, verify that (i) 2 2 tan tan 2 1 tan      (ii) 2 2 tan sin 2 1 tan      (iii) 2 2 1 tan cos 2 1 tan       (iv) cos 3 = 4 cos3  - 3 cos

Answer 1

Answer:

L.H.S. = sin 2A

Putting A = 30˚ in L.H.S. and R.H.S., we get

L.H.S. = sin 2 × 30˚= sin 60˚ = √3/2

R.H.S. = 2 × tan 30˚/1 + tan2 30˚ = (2 × 1/√3)/(1 + (1/√3)2

= (2/√3)/(1 + 1/3) = (2/√3)/(4/3)

= 2 × 3/√3 × 4 = √3/2

Hence,

L.H.S. = R.H.S.

Hence proved.