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If tanA=ntanB and sinA = msinB, then prove that cos^2A= m^-1 / n^+1

If tanA=ntanB and sinA = msinB, then prove that cos^2A= m^-1 / n^+1

Grade:10

1 Answers

sonika p
129 Points
4 years ago
sinA = msinB....(1)
tanA= ntanB
(sinA/cosA) = n(sinB/cosB)....(2)
substuting sinB value from equation (1)
cosB = (n/m) cosA......(3)
sin2A = m2sin2B
1-cos2A = m2(1-cos2B)
substituting equation (3)
1-cos2A = m2[1 – ((n2/m2)cos2A)]
1 – cos2A = m2 – n2cos2A
n2cos2A – cos2A = m2 – 1
cos2A = (m2 – 1)/(n2 – 1)
 

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