Trigonometry Answers

Frank and Marie set sail from the same point. Frank is sailing in the direction . Marie is sailing in the direction . After 11 hours, Marie was 5 miles due west of Frank. How far had Marie sailed?

I have two questions, both are verifying trigonometric identities, they are:

(secx - tanx)^2 + 1
---------------------- = 2tanx
csc(secx-tanx)

and

1 + cosx + sinx
--------------------- = secx + tanx
1 + cosx - sinx


please show all the steps to reach these two identities, and thank you so much for your help.

find q if x = ( sec q + tan q) and y = b( sec q - tan q)

A boat is headed at 115° and is traveling downstream at 28 mph. The stream is flowing S38°E at 11 mph. In what direction is the boat traveling? At what rate can it travel in still water?

2sin^2x-sinx=0

sin^2x+2cosx=2

4cos(x)=-1+cos(x)

tan(x)=2/3 and sec(x)=-sqrt13/3

tantheta/1-cos^2theta

solve this.
3 sin 2x = 2 sin x