Show that `tan^2 x = (1 - cos(2x))/(1 + cos(2x))`
- print Print
- list Cite
Expert Answers
justaguide
| Certified Educator
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
The identity `tan^2 x = (1 - cos(2x))/(1 + cos(2x))` has to be proved.
(The entire section contains 72 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- Cos (tan-1 x)
- 1 Educator Answer
- Find sin 2x, cos 2x, and tan 2x from the given information.Find sin 2x, cos 2x, and tan 2x from...
- 1 Educator Answer
- Prove tan x + cos x/(1+sin x) = 1/cos x
- 1 Educator Answer
- Prove that `sec^4(x)-tan^4(x)=1+tan^2(x)` .
- 2 Educator Answers
- how to prove tan^2x+cot^2x=2sec^x-1+cosec^2x-1=2
- 1 Educator Answer
vaaruni | Student
We are require to prove :- tan^2(x)= (1-cos2x)/(1+cos2x)
Let us take R.H.S -> (1-cos2x)/(1+cos2x)
(1-cos2x)/(1+cos2x)= {1-(1-2sin^2(2x))}/{(1+(2cos^2(2x)-1)}
[Using formula:- cos(2A)=1-2sin^2(A) Or cos(2A)=2cos^2(A)-1 ]
=> (1+cos2x)/(1-cos2x)=(1-1+2sin^2(x))/((1+2cos^2(x)-1))
=> (1+cos2x)/(1-cos2x)= 2sin^2(x)/2cos^2(x)
=> (1+cos2x)/(1-cos2x)= tan^2(x) <-- Proved
check Approved by eNotes Editorial
Student Answers