Trig Help dealing with identities Each expression simplifies

Trig Help dealing with identities! Each expression simplifies to a constant, a single trigonometric function or a power of a trigometric function. Use fundamental identities to simplify each expression.

sin(x)tan(x)/cos(x) =

(tan(x))^2+sin(x)csc(x) =

(sec(x))^21 =

Solution

1)sin(x)tan(x)/cos(x)

=tan(x)(sin(x)/cos(x))

=tan(x)tan(x)

=(tan(x))²

2)(tan(x))²+sin(x)csc(x)

=(tan(x))²+sin(x)(1/sin(x))

=(tan(x))²+1.................. [since sec²x -tan²x =1]

=(sec(x))²

3)(sec(x))²1.................. [since sec²x -tan²x =1]

=(tan(x))²