SOLUTION: Simplify the following trig expressions: 1. {cos(x)/1+sin(x)} + tan(X) 2. [sec(x) + csc(x)]/ [1+tan(x)] 3. [sin(x)+tan(x)]/ {(tan(x)(csc(x) +cot(x)} please help!

Algebra.Com
Question 362285: Simplify the following trig expressions:
1. {cos(x)/1+sin(x)} + tan(X)
2. [sec(x) + csc(x)]/ [1+tan(x)]
3. [sin(x)+tan(x)]/ {(tan(x)(csc(x) +cot(x)}
please help! if you can help me at least get started and show me the first few steps! thank you!

Found 2 solutions by robertb, stanbon:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
1. sec x. Multiply numerator and denominator of the 1st term by 1-sinx. The denominator will give . Simplify and combine the two fractions.
2. csc x. Convert everything in terms of sinx and cosx. This will give a complex fraction. combine fractions in the numerator, and do the same with the denominator. Terms will readily cancel.
3. sin x. Convert the cscx+ cotx as , and combine. Terms will readily cancel. simplify.

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Simplify the following trig expressions:
1. {cos(x)/1+sin(x)} + tan(X)
---
cos/(1+sin) + sin/cos
----
lcd = cos(1+sin)
----
= cos^2/lcd + sin(1+sin)/lcd
---
= [cos^2 + sin + sin^2]/lcd
---
= (1+sin]/[cos(1+sin)]
= 1/cos
====================================
2. [sec(x) + csc(x)]/ [1+tan(x)]
------
[1/cos + 1/sin ]/[1+sin/cos]
(sin+cos)/(sin*cos)] / (cos+sin)/cos]
----
(sin+cos)/(sin*cos)]
---
1/sin
===========================================

3. [sin(x)+tan(x)]/ {(tan(x)(csc(x) +cot(x)}
Change all terms to sines and cosines and see
if you can simplify.
=========================
Cheers,
Stan H.

RELATED QUESTIONS

Find the other five trigonometric functions for each of the following given: 1. sin ¢ =... (answered by Alan3354)
Find the remaining trigonometric ratios. cos(x) = − 1/5 , π < x < 3π/2 (answered by solver91311)
Choose the matching expression for -tan x cos x = A sin^2x/cos^2 x B. 1/sec^2 X... (answered by josgarithmetic,ikleyn)
Prove . (sin x + cos x)(tan x + cot x) = sec x + csc... (answered by math-vortex)
Find a numerical value of one trigonometric function of x if... (answered by lwsshak3)
Simplify: csc x/ tan x +cot... (answered by Alan3354)
(sec(x)-cos(x))(csc(x)-sin(x))=tan(x)/1+tan^2(x) please prove the identity,. do only one... (answered by Edwin McCravy)
I need help verifying these identities. {{{Sin(x)Cos(x)+Cos^2x =... (answered by Edwin McCravy)
Prove the following trig identity: tan x *sin^2 x + sin x*cos x = tan... (answered by greenestamps)