Question

If tan θ = n tan α,sin θ = m sin α, then prove that cos

Answer 1

Answer:

Step-by-step explanation:

sina=msinb

or, m=sina/sinb ---------(1)  and

tana=ntanb

or, sina/cosa=n(sinb/cosb)

or, n=sinacosb/cosasinb

or, n=m (cosb/cosa) -----(2)

or, ncosa=mcosb

or, n²cos²a=m²cos²b

or, n²cos²a=m²(1-sin²b) [∵, sin²a+cos²a=1]

or, n²cos²a=m²(1-sin²a/m²) [using (1)]

or, n²cos²a=m²{(m²-sin²a)/m²}

or, n²cos²a=m²-sin²a

or, n²cos²a=m²-(1-cos²a)

or, n²cos²a=m²-1+cos²a

or, n²cos²a-cos²a=m²-1

or, cos²a(n²-1)=m²-1