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)