Question

Given A=60 degree and b is equal to 30 degree prove that Cos A minus b is equals to cos a into cos b + sin a into sin b​

Answer 1

Answer:

A=60° B=30°

Cos(60°-30°)=cos60°×cos30°+sin60°×sin30°

cos30°=1/2×√3/2+√3/2×1/2

cos30°=√3/4+√3/4

cos30°=2√3/4

cos30°=√3/2

LHS. = RHS

Hence Proved.

Answer 2

To prove:

Cos(A-B)=CosAxCosB+SinAxSinB

Step-by-step explanation:

<A=60°

<B=30°

Cos(A-B)=Cos(60-30)=Cos30° — (I)

CosAxCosB+SinAxSinB

=Cos60xCos30+Sin60xSin30

=Cos60xCos30+Sin(90-30)xSin(90-60)

=Cos60xCos30+Cos60xCos30

=2xCos60xCos30

=2x1/2xCos30

=1xCos30

=Cos30° — (2)

From eq. (I) and (II),

Cos(A-B)=CosAxCosB+SinAxSinB

Hence Proved!