Question

simplify to a single trig function:\[{1+csc~x}\over{cos~x+cot~x}\]
it's supposed to be \(sec~x\)

Answer 1

@sauravshakya @ParthKohli @Hero @wasiqss

Answer 2

just get me started

Answer 3

Put everything in terms of sines and cosines

Answer 4

\[{1+{1\over sin~x}}\over{cos~x+{{cos~x}\over{sin~x}}}\]the part im stuck at is \[{sin~x+1}\over{cos^2x+cos~x}\]

Answer 5

Your second part is not completely correct

Answer 6

how?

Answer 7

It is correct except that instead of cos^2(x) in the denominator, it should be cos(x)sin(x)

Answer 8

yup^

Answer 9

so its \({sin~x+1}\over{cos~x~sin~x}\) ?

Answer 10

the denominator is cos(x)sin(x)+cos(x)

Answer 11

oh okay

Answer 12

how do i go from there?

Answer 13

and then you can factor out a cos(x) from the bottom, and you will then be able to cancel a few terms from the top

Answer 14

this makes a lot more sense now, thank you so much

Answer 15

i see where i went wrong...didnt simplify the fractions correctly