Simplify each expression to a single trig function or number
Asked by admin @ in Mathematics viewed by 301 People
Simplify each expression to a single trig function or number cosx(secx-cosx)
Answered by admin @
I did this test b4, yours is answer #number 12
Convert things to their basic forms.
Remember a few identities
sin^2 + cos^2 = 1 so
sin^2 = 1 - cos^2 and
cos^2 = 1 - sin^2
I'm going to skip typing the theta symbol, just to make things faster. Just assume it is there and fill it in as you work the problems.
Follow along to see how each problem was worked out. You'll catch on to the general technique.
======
1. sec θ sin θ
1/cos * sin = sin/cos = tan
2. cos θ tan θ
cos * sin/cos = sin
3. tan^2 θ- sec^2 θ
sin^2 / cos^2 - 1/cos^2
(sin^2 - 1)/cos^2
-(1-sin^2)/cos^2
-cos^2/cos^2
-1
4. 1- cos^2θ
sin^2
5. (1-cosθ)(1+cosθ)
Remember (a+b)(a--b) = a^2 - b^2
1-cos^2 = sin^2
6. (secx-1) (secx+1)
sec^2 -1
1/cos^2 - 1
1/cos^2 - cos^2/cos^2
(1-cos^2)/cos^2
sin^2/cos62
tan^2
7. (1/sin^2A)-(1/tan^2A)
1/sin^2 - 1/(sin^2/cos^2)
1/sin^2 - cos^2/sin^2
(1-cos^2)/sin^2
sin^2/sin^2
1
8. 1- (sin^2θ/tan^2θ)
1-sin^2/(sin^2/cos^2)
1 - sin^2*cos^2/sin^2
1-cos^2
sin^2
9. (1/cos^2θ)-(1/cot^2θ)
1/cos^2 - 1/(cos^2/sin^2)
1/cos^2 - sin^2/cos^2
(1-sin^2)/cos^2
cos^2/cos^2
1
10. cosθ (secθ-cosθ)
cos *(1/cos - cos)
1-cos^2
sin^2
11. cos^2A (sec^2A-1)
cos^2 * (1/cos^2 - 1)
1 - cos^2
sin^2
12. (1-cosx)(1+secx)(cosx)
(1-cos)(1+1/cos)cos
(1-cos)(cos + 1)
-(cos-1)(cos+1)
-(cos^2 - 1)
-(-sin^2)
sin^2
13. (sinxcosx)/(1-cos^2x)
sin*cos/sin^2
cos/sin
cot
14. (tan^2θ/secθ+1) +1
(sin^2/cos^2)/(1/cos) + 2
sin^2/cos + 2
sin*tan + 2
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