Question

If cos (0 + 20) = m cos 0, prove that : cot a = 1 + m tan (0 + a)
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Answer 1

Step-by-step explanation:

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