tan A=n tan B and sin A=m sin B.To prove (cos A)^2=(m^2-1)/(n^2-1)
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,349 answers
starTop subjects are Math, Science, and Business
You should remember that `tan A = sinA/cosA` and `tan B = sinB/cos B` , hence, substituting `m sin B` for `sin A ` in `tan A = n tan B` yields:
`tan A = n tan B =>sinA/cosA = n(sinB/cos B) => (m sin B)/cosA = n (sinB/cos B)`
Reducing by duplicate factors yields:
`m/cos A = n/cos B => (m/cos A)^2 = (n/cos B)^2`
`(cos A)^2 = (m/n)^2*cos^2 B`
Substituting `1 - sin^2B ` for `cos^2 B` yields:
`(cos A)^2 = (m/n)^2*(1 - sin^2B)`
Since `sin^2B = (sin^2A)/m^2` yields:
`(cos A)^2 = (m/n)^2*(1 - (sin^2A)/m^2)`
Hence, evaluating `(cos A)^2` under the given conditions yields `(cos A)^2 = (m/n)^2*(1 - (sin^2A)/m^2).`
Related Questions
- Prove tan x + cos x/(1+sin x) = 1/cos x
- 1 Educator Answer
- Prove the following reduction formula: integrate of ((cosx)^n) dx =1/n(cos^(n-1)x)(sin(x)) +...
- 2 Educator Answers
- Prove the following reduction formula: integrate of (tan^(n)x) dx= (tan^(n-1)x)/(n-1) - integrate...
- 2 Educator Answers
- if cos(A-B) + cos(B-C) + cos(C-A) = -3/2 Prove cos A + cos B + cos C = sin A + sin B + sin C = 0
- 1 Educator Answer
- Prove the double angle identity: `(1-tanA)/(1+tan A) = (cos 2A)/(1+sin 2A)` : 1-tan A...
- 1 Educator Answer
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.