Verify each identity

cot x = cos x / sin x

tan x = sin x / cos x

(Find common denominators)

cosx/sinx * cosx/cosx = cos^2x/sinxcosx

sinx/cosx * sinx/sinx = sin^2x/sinxcosx

(Now we can combine them)

csc / (sin^2x+cos^2x / sinxcosx)

(Simplify)

csc*sinx*cosx / sin^2x+cos^2x

sin^2x + cos^2x = 1

csc*sinx*cosx / (1)

csc*sinx*cosx

csc = 1/sinx

1/sinx*sinx = 1

(1)*cosx = cosx

answer; (& & );

which functions return a valid value without any arguments?

(-blank- and -blank- return a valid value without any arguments.)

1st -blank-

today

sqrt

count

2nd -blank-

round

now

sqrt