Question

Cosθ=nCos(θ+ 2Ø) Show that (n+1) tan(θ+Ø) =(n-1) cotØ​

Answer 1

Answer:

Correct option is

D

(

1+m

1−m

)cotϕ

cos(θ−ϕ)

cos(θ+ϕ)

=m

Apply componendo and dividendo

cos(θ+ϕ)−cos(θ−ϕ)

cos(θ+ϕ)+cos(θ−ϕ)

=

m−1

m+1

−(cos(θ−ϕ)−cos(θ+ϕ))

cos(θ+ϕ)+cos(θ−ϕ)

=

m−1

m+1

−2sin(θ)⋅sin(ϕ)

2cos(θ)⋅cos(ϕ)

=

m−1

1+m

2sin(θ)⋅sin(ϕ)

2cos(θ)⋅cos(ϕ)

=

1−m

1+m

cotθ⋅cotϕ=

1−m

1+m

tanθ=(

1+m

1−m

)⋅cotϕ