Chapter 2
3sin-1 x = sin -1 (3x - 4 x3), 1 1- ,2 2x ∈
3cos-1 x = cos -1 (4x3 - 3x), 1 , 12x ∈ Write the following functions in the simplest form: 3. 1 1 1tan x x − + − , x ≠ 0 4. 1 1 costan 1 cos x x − − + , 0 < x < π
1 cos sintan cos sin / x x / x x − − + , 4 −π < x < 3 π 6. 2 2 tan x a x − − , |x| < a 7. 2 3 3 2 3tan
| a | x | x |
|---|---|---|
| a ax − − − , a > 0; 3 3 − < <a a x Find the values of each of the following: 8. -1 -1 1tan 2cos 2sin 2 9. -1 -1 2 2 1 2 1tan sin cos² 1 1 x y x y −+ + + , | x | < 1, y > 0 and xy < 1 Find the values of each of the expressions in Exercises 16 to 18. 10. -1 2sin sin 3 π 11. -1 3tan tan 4 π 12. -1 -13 3tan sin cot5 2 + 13. 1 7cos cos is equal to6 − π |
(A) 7 / π (B) 5 / π (C) 3 / π (D) 6 π 14. 1 1sin sin ( )3 2 −π − − is equal to (A) 1 / 2 (B) 1 / 3 (C) 1 / 4 (D) 1 15. 1 1tan 3 cot ( 3)− −− − is equal to (A) π (B) 2 / π− (C) 0 (D) 2 3