Question

If tanA = a tanB and sinA= b sinB, prove that cos^2 A = b^2 - 1 / a^2 - 1
Please answer this.

Answer 1

sina=bsinb

or, b=sina/sinb ---------(1)  and

tana=ntanb

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

or, a=sinacosb/cosasinb

or, a=b (cosb/cosa) -----(2)

or, acosa=bcosb

or, a²cos²a=b²cos²b

or, a²cos²a=b²(1-sin²b) [∵, sin²a+cos²a=1]

or, a²cos²a=b²(1-sin²a/b²) [using (1)]

or, a²cos²a=b²{(b²-sin²a)/b²}

or, a²cos²a=b²-sin²a

or, a²cos²a=b²-(1-cos²a)

or, a²cos²a=b²-1+cos²a

or, a²cos²a-cos²a=b²-1

or, cos²a(a²-1)=b²-1

or, cos²a=(b²-1)/(a²-1)

Answer 2

Step-by-step explanation:

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