Question

if sin(theta + alpha) = cos(theta + alpha). find tan theta in terms of tan alpha

Answer 1

Answer:

sin(θ+α)=cos(θ+α)

sinθ.cosα+cosθ.sinα=cosθ.cosα−sinθ.sinα

Diving the complete equation by cosθ, and writing

cosθ

sinθ

=tanθ, we get

tanθ.cosα+sinα=cosα−tanθ.sinα

tanθ=

cosα+sinα

cosα−sinα

(ii)tan(π/4+θ).tan(π/4−θ)

1−tan(π/4).tanθ

tan(π/4)+tanθ

.

1+tan(π/4).tanθ

tan(π/4)−tanθ

1−tanθ

1+tanθ

.

1+tanθ

1−tanθ

=1