how can you prove this ..

1. sin˛ [theta] + cos˛ [theta]/cos˛ [theta] = |1/cos [theta]|˛

2. 1-cos˛[theta]/sin [theta] = sin [theta]_

3. 1+cot˛[theta]/csc ˛[theta]=1

4. csc˛ [theta]-1/csc˛[theta]=cos˛[theta]

5. cot [theta] – 1 =csc [theta] – sec [theta]/ sec [theta]

6. cos [theta] / sec [theta] + tan [theta] = 1-sin [theta]

7. csc˛[theta] = _cos ˛ [theta] + cot˛ [theta] + sin˛ [theta]

8. 2 cos˛ [theta]-1 =cos (4th power) [theta] –sin (4th power) [theta]

9. cos [theta]/1+sin [theta] + cos [theta] /1-sin [theta] = 2/ cos theta

10. sin (4th power) [theta]-1/cos ˛ [theta]=cos˛ [theta] -2