Question

if theta+phi=alpha and sin theta=k sin phi, prove that tan theta=k sin alpha/1+k cos alpha​

Answer 1

Answer:

Step-by-step explanation:

Sinθ = k sin∅

θ + ∅ = α

=> ∅ = α - θ

//substitute the above value in given equation.

Sinθ = k Sin∅

Sinθ = k Sin(α - θ)

//Remember sin(a-b)= sin a cos b-cos a sin b

Sinθ = k [SinαCosθ - CosαSinθ]

Sinθ + k CosαSinθ = k SinαCosθ

Sinθ [1+k Cosα] = k SinαCosθ

Sinθ / Cosθ = k Sinα / 1+k Cosα

Tanθ = k Sinα / 1+k Cosα

Hence proved...