Question

If A=30° , prove that :
(sin A - cos A)^2 = 1 - sin 2 A​

Answer 1

Step-by-step explanation:

Given=©

A=30°

Expression=©

(SinA-CosA)²=1-Sin2A

Solution=®

L.H.S.

=> (SinA-CosA)²

=>Sin²A+Cos²A-2SinACosA

[ By Sin2A= 2SinACosA]

=>1-Sin2A

As L.H.S. = R.H.S.

Hence Proved

Answer 2

Answer:

Step-by-step explanation:

From LHS

(sin30°-cos30°) ^2

(1/2-√3/2) ^2

(1/2) ^2+(√3/2)^2-2*1/2*√3/2

1/4+3/4-√3/2

1+3-2√3/4

4-2√3/4

2(2-√3) /4

2-√3/4

From RHS

1-sin2*30°

1-sin60°

1-√3/2

2-√3/2

LHS=RHS proved..