how to get the five trigonometric function of secA =2

Question

find the other five trigonometric function of sec A = 2

Answer 1

You get them as follows, using the definitions of the trig functions and the Pythagorean Identity:

1. sec A = 2  (GIven)
2. sec A = 1/cos A, so 1/cos A = 2.  Solve for cos A.
3. sin² A = 1 - cos² A.  Use your answer from 2 for  cos A to get sin A.
4. csc A = 1/sin A.  Use your answer from 3 for sin A
5. tan A = (sin A)/(cos A).  Use your answers from 2 and 3.
6. cot A = 1/tan A.  Use your answer from 5.

Remember to rationalize the denominators.