Question

if tan A = n tan B and sin A = m sin B, PROVE THAT COS SQUARE A = m2 - 1 / n2 - 1

Answer 1

Answer:

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

or, cos²a=(m²-1)/(n²-1)

Answer 2

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