Question

"Question25
If A = 30°, verify that : sin2A = 2 tan A / 1 + tan²A
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 289"

Answer 1

HELLO DEAR,

GIVEN THAT :-

A = 30°

now,

sin(2*30°) = sin60°

sin60° = √3/2 ( R.H.S)

NOW, L.H.S,

2tan30° / ( 1 + tan²30°)

= 2×√3/(1 + 1/3)

= 2√3/[(3 + 1)/3]

= 2√3(4/3)

= √3/2

hence,

R.H.S = L.H.S

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hey there!

Given to verify : sin2A = 2 tan A / 1 + tan²A

If A = 30°

1) sin 2A = sin (2*30) = sin60 = √3/2 [ T - Ratio of 60° , π/3 ]
2) tanA = tan30 = 1/√3

Now,
Given equation to verify : sin2A = 2 tan A / 1 + tan²A

==================================

Finding the value of sin2A

= sin60

= √3/2

==================================

Finding the value of 2 tan A / 1 + tan²A

= 2 tan30 / 1 +tan²30

= 2(1/√3 ) / 1 + (1/√3)²

= 2/√3 / ( 1 + 1/3 )

= 2/√3 / 4/3

= 2/√3 * 3/4

= √3/2

==================================

Here, We observe that sin2A = 2 tan A / 1 + tan²A

Hence proved that, sin2A = 2 tan A / 1 + tan²A for A = 30°