Question

Express tan θ in terms of tan α, if sin(θ + α) = cos (θ + α)

Answer 1

Please see the attachment

Answer 2

Answer:

Tanθ = (1 - tanα)/(1 + tanα)

Step-by-step explanation:

sin(θ + α) = cos (θ + α)

Using Sin( A + B) = SinACosB + CosASinB

& Cos(A + B) = CosACosB - SinASinB

=> SinθCosα + CosθSinα  = Cosθcosα - SinθSinα

=> SinθCosα  + SinθSinα = Cosθcosα - CosθSinα

=> Sinθ (Cosα  + Sinα) = Cosθ(Cosα  - Sinα)

=> SinθCosα(1 + tanα) = CosθCosα(1 - tanα)

Dividing both sides by CosθCosα

=> Tanθ(1 + tanα) = (1 - tanα)

=> Tanθ = (1 - tanα)/(1 + tanα)