Asked by Sandra
Simplify the follow)ing to the simplest form
(tan(x) +cot(x))/ (tan(x)*cot(x))
(tan(x) +cot(x))/ (tan(x)*cot(x))
Answers
Answered by
Reiny
I usually change everything to sines and cosines
(tan(x) +cot(x))/ (tan(x)*cot(x))
= (sinx/cosx + cosx/sinx) / (sinx/cosx * cosx/sinx)
= (sin^2 x + cos^2 x)/(sinxcosx) / 1
= 1/(sinxcosx) ----> I know 2sinxcosx = sin 2x
so sinxcosx = (1/2)sin2x
= 2/sin 2x or 2 csc 2x
or from the original:
1/(sinxcosx) = cscx secx
(tan(x) +cot(x))/ (tan(x)*cot(x))
= (sinx/cosx + cosx/sinx) / (sinx/cosx * cosx/sinx)
= (sin^2 x + cos^2 x)/(sinxcosx) / 1
= 1/(sinxcosx) ----> I know 2sinxcosx = sin 2x
so sinxcosx = (1/2)sin2x
= 2/sin 2x or 2 csc 2x
or from the original:
1/(sinxcosx) = cscx secx