Simplify cos t csc t cot theta csc theta sin theta sin x

Simplify cos t csc t cot theta / csc theta - sin theta sin x / csc x + cos x / sec x

Solution

( a)

given cost cosect

==> cost . 1/sint

===> cost/sint ==> cot t

( b )cot( theta ) / csc(theta)-sin(theta)

==> cos(theta)/sin(theta) / 1/sin(theta) - sin(theta)

===> cos(theta)/sin(theta) (sin(theta) ) / 1 - sin^2(theta)

==> cos(theta) / 1-sin^2(theta)

===> cos(theta) / (1-sin(theta) ( 1+ sin(theta)

( c ) sinx / cscx + cosx / secx

===> sinx / 1/sinx + cosx / 1/cosx

===> sin^2x + cos^2x ==>1