Help with precalc please?

precalc

#1

Help with precalc please?

Answer:

Use x for theta
1. a.cot^2x/cscx-1(Given)
b. Use pythagorean identity: cot^2x=csc^2x-1
c. Rewrite it: csc^2x-1/cscx-1
d. Cancel 1 of the cscx-1 on the top with the bottom
e. You are left with cscx-1 and that is your answer :slight_smile:

2. a. sinx/1+cosx + 1+cosx/sinx
b. Make a common denominator: sin^2x/(1+cosx)(sinx) + cos^x+2cosx+1/(1+cosx)(sinx)
c. Combine the 2 fractions
d. sin^2x+cos^2x+2cosx+1/(1+cosx)(sinx)
e.Use pythagorean identity: sin^2x+cos^x=1
f. Rewrite it: 1+2cosx+1/(1+cosx)(sinx)
g. Add the 1s: 2+2cosx/(1+cosx)(sinx)
h. Factor out the 2 and rewrite it: 2(1+cosx)/(1+cosx)(sinx)
i. Cancel the 1+cosx on the top with the one on the bottom
j. Rewrite: 2/sinx
k. Use the reciprocal identity: sinx=1/cscx
l. Rewrite: 2/1/cscx
m. Flip and multiply: 2*csx
n. =2cscx :slight_smile:

3. I haven’t learned inequalities so just google it and i’m sure you’ll find it.