Question

"Question29
Using the formula, sin A = √1-cos2 A/2 , find the value of sin 30° , it being given that cos 60° = 1/2
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 289"

Answer 1

Hey there !

Given Formula : sinA = √1 - cos2A / 2
Also, cos60 = 1/2
Required to find : sin30

Now,
Let A = 30 , 2A = 60°

sinA = √1 - cos2A / 2

sin30 = √( 1 - 1/2 ) / 2

sin30 = √(1/2)/2

sin30 = √(1/4) = 1/2

Therefore , sin30 = $\frac {1 } { 2 }$

Thanks for the question!

Answer 2

Heya ,

Acc. to the question,

Putting A = 30°

2A = 60°

Sin30° = √1 - cos60° / 2

Squaring both sides, we get,

sin² 30° = 1 - cos60° / 2 = 1 - 1/ 2 /2 = 1/4

Sin30° = √1/4

Sin30° = 1/2

Thanks!!