Question

"Question26
If A = 30° , Verify that : cos 2A = 1- tan²A / 1 + tan²A
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 289"

Answer 1

HELLO DEAR,

GIVEN THAT:-

A = 30°

NOW,

cos (2*30°) = cos60°

= cos60°

= 1/2

NOW,

(1 - tan²A)/(1 + tan²A)

= (1 - tan²30°)/(1 + tan²30°)

= (1 - 1/3) / ( 1 + 1/3)

= [(3 - 1)/3] / [ (3 + 1)/3]

= (2/3) / (4/3)

= 2/3 * 3/4

= 1/2


hence , verified


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hey there!

Given to verify : cos 2A = 1- tan²A / 1 + tan²A

If A = 30°

1) cos 2A = cos (2*30) = cos60 = 1/2 [ T - Ratio of 60° , π/3 ]
2) tanA = tan30 = 1/√3

Now,
Given equation to verify : cos 2A = 1- tan²A / 1 + tan²A
==================================

Finding the value of cos2A

= cos60

= 1/2

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

Finding the value of 1 - tan²A / 1 + tan²A

= 1 - tan²30 / 1 +tan²30

= 1 - (1/√3)² / 1 + (1/√3)²

= 1 - 1/3 / ( 1 + 1/3 )

= (2/3) / (4/3)

= 2/3 * 3/4

= 1/2

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

Here, We observe that cos 2A = 1- tan²A / 1 + tan²A

Hence proved that, cos 2A = 1- tan²A / 1 + tan²A for A = 30°