Find

Sina=m×sinb , tanb=n×tana so find

M×M-1÷n×n-1=?

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)

Regards
Arun (askIITians forum expert)