Question

last question is = 2sin 30° cos30° = sin60°

Answer 1

Step-by-step explanation:

20.

LHS

cos60°.cos30°-sin60°.sin30°

we know that

cos60°=sin30°=1/2

and

sin60=cos30=√3/2

so LHS=>

(1/2)(√3/2)-(1/2)(√3/2)

√3/4-√3/4

0

=cos90° = RHS

HENCE PROVED

21.

LHS

cosAcosB+sinAsinB

here, A=60° B=30°

so

LHS=>

cos60°cos30°+sin60°sin30°

(1/2)(√3/2)+(√3/2)(1/2)

√3/4+√3/4

√3/2 = cos30 = cos(60-30) = cos(A-B)

=RHS

HENCE PROVED

21.

LHS

2 sin30° cos30°

=> 2 (1/2) (√3/2)

√3/2 = sin60°

=RHS

HENCE PROVED

Answer 2

Answer:

L.H.S=2*1/2*√3/2=1*√3/2=√3/2=R.H.S

Step-by-step explanation:

LHS=2*1/2*√3/2 =1*√3/2 =√3/2 =RHS