Asked by Sharon
We have to solve for the problem below to make sure that it is equivalent to 2csc(x). However, I keep getting 2/2sin(x) and not 2/sin(x), which is what 2csc(x) is.
tan(x)/(1+sec(x))+ (1+sec(x))/tan(x)= 2csc(x)
tan(x)/(1+sec(x))+ (1+sec(x))/tan(x)= 2csc(x)
Answers
Answered by
drwls
tan(x)/(1+sec(x))+ (1+sec(x))/tan(x)
= tan x/[(cosx+1)/cosx]
+ [(cosx+1)/cosx]/tanx
= sin x/(cosx+1) + (cosx +1)/sinx
= [sin^2 x + (cosx +1)^2]/[sinx(1 + cosx)]
= (sin^2x + cos^2x + 2 cos x + 1)/[sinx(1 + cosx)]
= 2 (1 + cosx)/[sinx(1 + cosx)]
= 2/sin x = 2 csc x
= tan x/[(cosx+1)/cosx]
+ [(cosx+1)/cosx]/tanx
= sin x/(cosx+1) + (cosx +1)/sinx
= [sin^2 x + (cosx +1)^2]/[sinx(1 + cosx)]
= (sin^2x + cos^2x + 2 cos x + 1)/[sinx(1 + cosx)]
= 2 (1 + cosx)/[sinx(1 + cosx)]
= 2/sin x = 2 csc x
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.