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