Asked by SkiMasktheSlumpGod
tanx cotx
------- + ------- = 1 +secxcscx
1 - cotx 1- tanx
prove the proof
------- + ------- = 1 +secxcscx
1 - cotx 1- tanx
prove the proof
Answers
Answered by
Steve
tanx/(1-cotx) + cotx/(1-tanx)
= tanx/(1-cotx) + cotx/(1-tanx) * (-tanx/-tanx)
= tanx/(1-cotx) - tan^2x/(1-tanx)
= (cotx-tan^2x)/(1-tanx)
= (1-tan^3x)/(tanx(1-tanx))
= (1-tanx)(1+tanx+tan^2x) / (1-tanx)(tanx)
= (1+tanx+tan^2x)/tanx
= 1/tanx + 1 + tanx
= 1 + sinx/cosx + cosx/sinx
= 1 + (sin^2x+cos^2x)/(sinx cosx)
= 1 + secx cscx
= tanx/(1-cotx) + cotx/(1-tanx) * (-tanx/-tanx)
= tanx/(1-cotx) - tan^2x/(1-tanx)
= (cotx-tan^2x)/(1-tanx)
= (1-tan^3x)/(tanx(1-tanx))
= (1-tanx)(1+tanx+tan^2x) / (1-tanx)(tanx)
= (1+tanx+tan^2x)/tanx
= 1/tanx + 1 + tanx
= 1 + sinx/cosx + cosx/sinx
= 1 + (sin^2x+cos^2x)/(sinx cosx)
= 1 + secx cscx
Answered by
Steve
oops . typo in line 2, but you should be able to catch it.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.