Please answer this question from trignometry
Answers
Here's the answer you are looking for
SinA = mSinB
m/SinA = 1/SinB
As 1/Sinθ = Cosecθ
So, CosecB = m/SinA --------------1
Similarly,
TanA = nTanB
1/TanB = n/TanA
As Cotθ = 1/Tanθ
Therefore, CotB = n/TanA ---------------2
We know,
Cosec^2θ - Cot^2θ = 1
Thus, Cosec^2B - Cot^2B = 1
Substituting the value of CosecB and CotB from equation 1 and equation 2
(m/SinA)^2 - (n/TanA)^2 = 1
m^2/Sin^2A - n^2 Cos^2A/Sin^2A = 1 (As Tan^2A = Sin^2A/Cos^2A)
m^2 - n^2 Cos^2A = Sin^2A
m^2 - n^2 Cos^2A = 1 - Cos^2A (Sin^2A = 1 - Cos^2A)
n^2Cos^2A - Cos^2A = m^2 - 1
Cos^2A (n^2 - 1) = m^2 - 1
Cos^2A = (m^2 - 1) / (n^2 - 1)
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