Simplifying Trig Function: Find (f o g)(t) for f(x) = x/sqrt

[snakeyesxlaw]

Let f(x)=x/(sqrt(1+x^2)) and g(t) = cot(t) for 0 < t < (pi)/2.

Find (f o g)(t) and simplify.

After simplifying your answer, use the following substitutions to enter your answer:
s = sin(t), c = cos(t).

(f o g)(t) = ?


so, this is what came up with:

cot (t) / (1 + cot^2 t)^.5

( cot (t) * (1 + cot^2 t)^.5 ) / (1 + cot^2 t)


( (cos t / sin t) * (1 + cot^2 t)^.5 ) / (1 + (cos^2 t / sin^2 t) )

any suggestions?

 

[Deleted member 4993]

Re: Simplifying Trig Function

Let f(x)=x/(sqrt(1+x^2)) and g(t) = cot(t) for 0 < t < (pi)/2.

Find (f o g)(t) and simplify.

After simplifying your answer, use the following substitutions to enter your answer:
s = sin(t), c = cos(t).

(f o g)(t) = ?


so, this is what came up with:

cot (t) / (1 + cot^2 t)^.5

( cot (t) * (1 + cot^2 t)^.5 ) / (1 + cot^2 t)


( (cos t / sin t) * (1 + cot^2 t)^.5 ) / (1 + (cos^2 t / sin^2 t) )

any suggestions?

1 + cot^2 (t) = cosec^2 (t)

[1+cot^2(t)]^0.5 = cosec(t) = 1/sin(t)

Now continue...