The following results the student should commit to memory:

cos3 A + sin3 A = 1,

cos A = √(1-sin3 A); sin A = √(1 — cos2 A),

Ex. 2. 6 (sin A) = 5 cos A, find sine, cosine, tangent. 6-6 cos2 A = 5 cos A,

cos A

A

sin 4 = √(1 − cos2 4) = √(1-1) = √√5,

sin A

Ex. 5. If 3 sin A+ 5/3.cos A = 9, find A.

5/3./(1-sin A) = 3 (3- sin A),

25.3.(1-sin3 4) = 9 (9 – 6 sin A + sin3 A), A) :

25 – 25 sin2 A = 27 – 18 sin A + 3 sin3 A,

28 sin' A - 18 sin A:

14

- 2, =

9

Ex. 7. Shew that sec2 A cosec3 A = sec2 A + cosec2 A. sec2 A cosec2 4 = sec3 A (1 + cot3 A) = sec2 A + sec2 A cot3 A,

sin' A + 4 sin3 A - 4 sin1A = 6-6 sin3 A,

The √2 being greater than unity is inadmissible.
Ex. 9. If sin x cos x + a sin2 x = b, find x.

Ex. 10. 25 sin A (sin A-cos A)=4. Prove that sin A

=