Question

If cos(θ+Φ)=mcos(θ-Φ),then prove that tanθ=1-m/1+mcotΦ
​

Answer 1

Step-by-step explanation:

ANSWER

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

Answer By

Answer 2

Step-by-step explanation:

The above answer will surely help You...