Question 960989
{{{ g(x) = (x) sqrt(64x^2+25) }}} and {{{ h(t)=(5/8)cot(t) }}}
<pre>
{{{ g(h(x)^"")}}}{{{""=""}}}{{{(expr(5/8)^""cot(t)) sqrt(64(expr(5/8)^""cot(t))^2+25) }}}{{{""=""}}}{{{(expr(5/8)^""cot(t)) sqrt(64(expr(25/64)^""cot^2(t))+25) }}}{{{""=""}}}

{{{expr(5/8)^""cot(t)* sqrt(64*expr(25/64)^""cot^2(t)+25) }}}{{{""=""}}}{{{expr(5/8)^""cot(t)* sqrt(cross(64)*expr(25/cross(64))^""cot^2(t)+25) }}}{{{""=""}}}{{{expr(5/8)^""cot(t)*sqrt(25cot^2(t)+25) }}}{{{""=""}}}

{{{expr(5/8)^""cot(t) sqrt(25(cot^2(t)+1)) }}}{{{""=""}}}{{{expr(5/8)^""cot(t)*5*sqrt(cot^2(t)+1) }}}{{{""=""}}}{{{expr(25/8)^""cot(t)*sqrt(cot^2(t)+1) }}}{{{""=""}}}

There is an identity {{{1+cot^2(theta)=csc^2(theta)}}}

{{{expr(25/8)^""cot(t)*sqrt(csc^2(t)) }}}{{{""=""}}}

{{{expr(25/8)^""cot(t)*abs(csc(t)) }}}{{{""=""}}}

Since t is in the first quadrant we can eliminate the absolute value:

{{{expr(25/8)^""cot(t)*csc(t) }}}{{{""=""}}}

Use identities {{{cot(theta)=cos(theta)/sin(theta)}}} and {{{csc(theta)=1/sin(theta)}}}

{{{expr(25/8)expr(cos(t)/sin(t))*expr(1/sin(t)) }}}{{{""=""}}}

{{{25cos(t)/8sin^2(t)}}}

Edwin</pre>