Question

can someone help me with trig identity proof please? Work and question attached.

Answer 1

not sure if I did this right since I couldn't go on any further

Answer 2

Youre making it too complex. I have a different trick to do it which works at most times. See the point here is to bring it in its simplest form, both the lhs and rhs. therefore as csc = 1/sin, simplify the lhs similarly to solve it.
Never make it too complex. I used to do taht tons of times :)

Answer 3

Yeah I wanted to do that but my teacher said that we are only suppose to simplify the lhs, and through that get to the rhs answer.

Answer 4

It can still be done. See, first simplify the lhs. When you keep simplifying it you will get ((sin x+cosx)/cosxsinx)/1+tan x
now simplify 1+tan x you get cosx+sinx / cosx
Now do the cancellation
and you will have cosx/cosxsinx
you are left with 1/sinx which is cscx
There you go, the answer. With no need to do all the csc and sec ;)

Answer 5

If you see that it's not going the right way. start over with another method

Answer 6

Mathbreaker is right, but if your teacher doesnt want you to change into signs and cosigns then just combine the bottom and cancel. done in three steps.

Answer 7

If you dont have to, you can still do it, you made a mistake there. 1+ secx / csc x is equal to cscx + secx / csc x, which then cancels out similarly to give you csc x as the direct answer.

Answer 8

Ok thanks for the tips. I was able to solve it using your method Mathbreaker. It cleared up finally, and I cancelled out the things to get 1/sinx in the end. Thanks for the help

Answer 9

Youre welcome :)
All the best :D