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
Answers
Answered by
11
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.
Answered by
6
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!
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