SOLUTION: Simplify each trig expression into 1 term: 1.) sin(theta)+cos(theta)cot(theta) 2.)cos^2(theta)+tan^2(theta)cos^2(theta) Verify each identity: 3.) sec(theta)sin(theta)cot(the

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Question 756302: Simplify each trig expression into 1 term:
1.) sin(theta)+cos(theta)cot(theta)
2.)cos^2(theta)+tan^2(theta)cos^2(theta)
Verify each identity:
3.) sec(theta)sin(theta)cot(theta)=1
4.)csc^2(theta)-cot^2(theta)=1
5.)sin^2(theta)
------------
1-cos(theta) = 1+cos(theta)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Simplify each trig expression into 1 term:
1.) sin(theta)+cos(theta)cot(theta)
----
sin(x) + cos(x*(cos/sin)
----
= (sin^2(x) + cos^2(x))/sin(x) = 1/sin(x) = csc(x)
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2.)cos^2(theta)+tan^2(theta)cos^2(theta)
----
cos^2(x) + [sin^2(x)/cos^2(x)*cos^2(x)]
----
= cos^2(x) + sin^2(x)
-----
= 1
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Verify each identity:
3.) sec(theta)sin(theta)cot(theta)=1
(1/cos)*sin)(cos/sin) = 1
Cancel all factors common to numerator and denominator:
1 = 1
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4.)csc^2(theta)-cot^2(theta)=1
(1/sin^2 - [cos^2/sin^2] = 1
---
(1-cos^2)/sin^2 = 1
---
sin^2/sin^2 = 1
1 = 1
========================
5.) [sin^2(x)/(1-cos(x)] = (1+cos(x)
-------
Cross-multiply to get:
sin^2 = (1-cos)(1+cos)
---
sin^2 = 1-cos^2
---
sin^2 = sin^2
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Cheers,
Stan H.
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