"Question25
If A = 30°, verify that : sin2A = 2 tan A / 1 + tan²A
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 289"
Answers
Answered by
119
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
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
Answered by
54
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°
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°
Similar questions
Hindi,
7 months ago
Social Sciences,
7 months ago
Social Sciences,
7 months ago
Music,
1 year ago
Physics,
1 year ago
English,
1 year ago