7. a) Using exact values, verify the following identity for 0-60°: [T 2]
1+ cot20
csc² 0.
b) State the restrictions for 0, 0° 0≤360°. [T 2]
c) Prove the identity for all values of 0 which satisfy the restrictions. [T 2]
8. Prove the identity: (cot x) (cos x) + sin x csc x. [T 2]
9. For each of the following questions state whether the statement is true or false. Justify
your answer.
a) sec² 0 + csc² 0 sec² 0 csc2 0; [C 4]
b) tan 270° cot 270° = 1. [C 4]
10. Simplify: (1 - cos 0) (1 + cos 0). [K/U=4]
Lohan St-AL
aniwollo
12. Prove the identity: tan²x cos²x =
(sec2x-1) (1- sin x)
1 + sin²x
[T=4]
13. Prove each of the following identities. Show all work!
ham à A à-ATLS on esititnobi Jedi
a) sec² + csc² = sec² 0 csc² 0 [c=4]
(1-8209) (1-0 nia
cos B
b).
+
1 + cos 0
cos
1- cos
=2cot 8 csc 0. [A=4]
14. Prove the following identity. Show all the steps of your solution. [T/I=3]
1 - tan² 0
= 1 + cot 0.
tan - tan²
15. Prove the following identity. Use proper notation for full marks. [T=5]
tan 6 - sec
sin30 + cos20 sin 0
1 - sin20
16. If tan² 0 - 2 tan 0-3 = 0, find all possible values of 6, where 0° ≤0≤360°. [T=5]