Question

Prove that ,
sin(theta+π/6)-sin(theta-π/6)=cos theta

Answer 1

Answer:

Step-by-step explanation:

sin(theta+π/6)-sin(theta-π/6)=cos theta

L.H.S

Sin(θ + 30) - Sin(θ - 30)

We know that SIn(A+B) = SinACosB + CosASinB

                        Sin(A-B) = SinACosB - CosASinB

= SInθCos30 + CosθSin30 - [SinθCos30 - CosθSin30]

= SInθCos30 + CosθSin30 - SinθCos30 + CosθSin30

= 2CosθSin30

= 2Cosθ * 1/2 ( ∵ Sin 30 = 1/2)

= Cosθ

= R.H.S

Hence proved.