Question

If A=30, prove that

sin2a = 2 tan A / (1 + tan2 A) ​

Answer 1

Step-by-step explanation:

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.

Answer 2

2tanA/(1 + tan²A)

= 2 (sinA/cosA)/ (1 + sin²A/cos²A)

= (2 sinA/cosA)/(cos²A + sin²A)/cos²A

= (2sinA/cosA)/(1/cos²A)

= 2sinA.cosA

= sin2A hence proved,,