One of the most important and exam oriented question from trigonometry, topic – trigonometric identities in which we have given that tanA=ntanB and also sinA=msinB, we have to prove that cos²A= (m²-1)/(n²-1)

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 13B, question no 14

## sinA=msinB⟶(1)

tanA=ntanB

sinA/cosA = nsinB/cosB⟶(2)

Substituting sinB from equation 1, we get

⟹cosB=n/m cosA⟶(3)

sin²A=m²sin²B

1−cos²A = m²(1−cos²B)

Substituting equation 3, we get

1−cos²A = m²(1−m²n²cos²A),

cos²A = (m²−1)/(n²-1) (proved)