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Factor And Simplify Trig Expressions Help

How do I factor and simplify these trigonometric expressions?

I don't get how to do these... I can factor the ones NOT involving stuff to the third power, but I don't know what to do when it IS to the third power! HELP! Can you please explain what you do, step-by-step?

a) sin^3x + 27
b) 1 - 125tan^3x


for a), I got (sin x + 3)^3 because I just took the 3rd root of everything... and then I wrote it to the third power, but the book says that that is wrong.

for b) I did something similar and got (1 - 5tan x)^3, but again, that is wrong!

What am I doing here?!! Better yet, what SHOULD I be doing? Thanks so much! I'll pick a best answer TODAY!!!!!!

Simplify trig expression 1+cscx / cosx+cotx?

(1 + cscx) / (cosx + cotx) =

rewrite cscx and cotx in terms of sinx, cosx:

[1 + (1/sinx)] / [cosx + (cosx/sinx)] =

let sinx be the common denominator:

[(sinx + 1)/sinx] / [(sinx cosx + cosx)/sinx] =

[(sinx + 1)/sinx] [sinx / (sinx cosx + cosx)] =

cancel sinx out:

[(sinx + 1)/ (sinx cosx + cosx)] =

factor out cosx from the denominator:

[(sinx + 1)/ cosx (sinx + 1)] =

cancel (sinx + 1) out:

1/ cosx = secx


I hope it helps...
Bye!

Factor the expression and use the fundamental identities to simplify (trig)?

1. cot^2x(1-cos^2x) (this one i don't know where to go from here)

2. sec^2x(tan^2x +1) = 1/cos^2x(cos^2x/sin^2x+1) (then the two cos^2x cancel)
= 1/sin^2x +1 = cscx +1

________
1. (sinx+cosx) ^2 = sin^2x+cos^2x =1
2. cot^2x -cscx cotx + cscx cotx -csc^2x (then the two middle cscx cotx cancel)
= cot^2x - csc^2x (i'm not sure if this one is finished)


I hope the two I did finish help and maybe you can work on what I did for the other two

Can I simplify this trigonometric expression like this?

yes

Need help with simplifying trig equations?

1.

sec²θ = tan²θ + 1

((tanθ+1)(tanθ+1)−sec²θ) / tanθ
= ((tan²θ + 2 tanθ + 1) − (tan²θ + 1)) / tanθ
= 2 tanθ / tanθ
= 2

2.

Factor quadratic expression in cosθ the same way you would factor a quadratic expression in x:

5 cos²θ + 6 cosθ + 1
= 5 cos²θ + 5 cosθ + cosθ + 1
= 5 cosθ (cosθ + 1) + 1 (cosθ + 1)
= (cosθ + 1) (5 cosθ + 1)

Also cos²θ−1 factors as (cosθ−1)(cosθ+1) and not as cosθ(cosθ−1)

(5 cos²θ + 6 cosθ + 1) / (cos²θ − 1)
= (cosθ + 1) (5 cosθ + 1) / ((cosθ − 1) (cosθ + 1))
= (5 cosθ + 1) / (cosθ − 1)
= 5 + 6/(cosθ − 1)

3.

sec²θ = cot²θ + 1

(1 + cotθ) (1 − cotθ) − csc²θ
= 1 − cot²θ − (cot²θ + 1)
= −2 cot²θ

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