SOLUTION: Let f (x) = (1/(x^2 sqrt(49 + x^2)) and g(t) = 7 tan (t) for 0 < t < pi/2 Find (f � g)(t) and simplify so that there are no radicals in the function. Write your answer in t

Question 929358: Let f (x) = (1/(x^2 sqrt(49 + x^2))
and g(t) = 7 tan (t)
for 0 < t < pi/2

Find (f � g)(t) and simplify so that there are no radicals in the function. Write your answer in terms of sin(t) and cos(t).
(f � g)(t) =
THANKS!
Please explain
THANKS!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let f (x) = (1/(x^2 sqrt(49 + x^2))
and g(t) = 7 tan (t) for 0 < t < pi/2
Find (f � g)(t) and simplify so that there are no radicals in the function. Write your answer in terms of sin(t) and cos(t).
(f � g)(t) = f[g(t)] = f[7*tan(t)]
---------
= 1/[(7tan(t))^2*sqrt(49 + (7*tan(t))^2)]
---------
= 1/[49tan^2(t)*sqrt(49 + 49tan^2(t)]
---------
= 1/[49tan^2(t)*7sqrt(1+tan^2(t)]
= 1/[49tan^2(t)*7sec(t)]
= 1/[343 *sin^2(t)/cos^3(t)]
-------------
Cheers,
Stan H.
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