Proving (csc x + cot x)/(tan x + sin x)=cot x*csc x with SOHCAHTOA

[wes28]

Homework Statement

I am supposed to show that this statement holds true

(csc x + cot x) / (tan x + sin x) = cot x * csc x
using sohcahtoa

Homework Equations

The Attempt at a Solution

I have tried this

(( h/o ) + (a/o ) / ( o/a + o/h)) 1st

(( ah / o sqrd )) + ((ah / o sqrd )) 2nd

(ah + ah) / (o sqrd) 3rd

after this I cannot see where to go, to show that it
equals cot x * csc x

 

[praharmitra]

do u know how to express all the trigonometric functions in terms of sin and cos??

If you do, then replace each trig func, with its corresponding sin and cos representation, and simplify both sides separately

Thats one of the ways t do it.

PS - U may also need to use a very important identity concerning sines and cosines

1. $$sin^2(x) + cos^2(x) = 1$$

Can you prove the above identity? (note: that can be done in the method you have already applied to tackle the problem initially)

 

[praharmitra]

do u know how to express all the trigonometric functions in terms of sin and cos??

If you do, then replace each trig func, with its corresponding sin and cos representation, and simplify both sides separately

Thats one of the ways t do it.

PS - U may also need to use a very important identity concerning sines and cosines

1. $$sin^2(x) + cos^2(x) = 1$$

Can you prove the above identity? (note: that can be done in the method you have already applied to tackle the problem initially)