Trig identities help

G

Guest

Guest
simplify csc x cos2 x/1+csc x
the tiny 2 means squared
answer choices include
csc x + 1
1+sin x
1-sin x
sin x -1

thanks :lol:
 
Is the expression as follow?

. . . . .(csc(x)cos<sup>2</sup>(x))/(1 + csc(x))

A good first step would be to convert everything to sines and cosines, and see where you can go from there.

Eliz.
 
i still need help but the expression is express that way i tried changing everything to sine and cosine but the denumator is kind of hard please give more help :lol:
 
Since the cosecant is the reciprocal of the sine, then:

. . . . .1 + csc(x) = 1 + 1/sin(x) = [sin(x) + 1]/sin(x)

Rearrange the numerator similarly, and then (since you're dividing now by a fraction) flip and multiply. Then simplify.

Eliz.
 
Did as you said but my answer ended up being cos^2x/sin^2x which can be simplify into cot^2x but that's not in my answer choices. Did i did something wrong
 
I'm sorry, but I can't help you find your errors until you post your work.

Eliz.
 
for the numerator i did (1/sinx)(cos^2/1) because the cscx can be changed to 1/sinx. I mutiply it out and got cos^2x/sinx. For the denominator i did (sinx)/(sinx+1) dividing the numerator from denominator by flipping as you suggested i got (cos^2x)(sinx)/(sin^2x+sinx) I cancel the two sines i from top and oone from bottom and got cos^2x on the top over sin^2x on the denominator but that's wrong can you explain why
 
You had the fraction:

. . . . .[cos<sup>2</sup>(x)sin(x)] / [sin(x)(sin(x) + 1)]

How did you cancel off the common factor of sin(x) and end up with a denominator of sin<sup>2</sup>(x) instead of sin(x) + 1?

Eliz.
 
I made a mistake and didn't cancel sinx out instead i multiply it out but even if i cancel out sinx i would still end up with cos^2x/sinx+1 and what's the next step in simplifying
 
Use the Pythagorean Identity, sin<sup>2</sup>(x) + cos<sup>2</sup>(x) = 1, to replace the cosine. Then factor the difference of squares, and cancel the common factor. You'll get one of the listed answers.

Eliz.
 
when i replace cosine with 1-sine^2 i got 1-sin^2x(sinx)/sinx(sinx+1) i HAVE NO IDEA THE NEXT STEP
 
What is the factorization of 1 - sin<sup>2</sup>(x)? (Hint: Use the difference-of-squares formula.)

Eliz.
 
You must log in or register to reply here.
Top