Prove the following: 1. 3sin1 x = sin1 (3x 4x3), 1 1 , 2 2 x 2. 3cos1 x = cos1 (4x3 3x), 1 , 1 2 x 3. tan1 1 1 2 7 1 tan tan 11 24 2 + = 4. 1 1 1 1 1 31 2 tan tan tan 2 7 17 + = Write the following functions in the simplest form: 5. 2 1 1 1 tan x x + , x 0 6. 1 2 1 tan x 1 , |x| > 1 7. 1 1 cos tan 1 cos x x + , 0 < x < p 8. 1 cos sin tan cos sin x x x x + , 4 p < x < 3 4 p 9. 1 2 2 tan x a x , |x| < a 10. 2 3 1 3 2 3 tan 3 a x x a ax , a > 0; 3 3 < < a a x Find the values of each of the following: 11. 1 1 1 tan 2cos 2sin 2 12. cot (tan1a + cot1a) 13. 2 1 1 2 2 1 2 1 tan sin cos 2 1 1 x y x y + +
Prove the following:
Question 1:3sin–1 x = sin–1 (3x – 4x3), 1 1 – , 2 2 x Î
Question 2:3cos–1 x = cos–1 (4x3 – 3x), 1 , 1 2 x Î
Question 3:tan–1 1 1 2 7 1 tan tan 11 24 2 − − + =
Question 4:1 1 1 1 1 31 2 tan tan tan 2 7 17 − − − + = Write the following functions in the simplest form:
Question 5:2 1 1 1 tan x x − + − , x ¹ 0
Question 6:1 2 1 tan x 1 − − , |x| > 1
Question 7:1 1 cos tan 1 cos x x − −
+ , 0 < x < π
Question 8:1 cos sin tan cos sin x x x x − −
+ , 4 −p < x < 3 4 p
Question 9:1 2 2 tan x a x − − , |x| < a
Question 10:2 3 1 3 2 3 tan 3 a x x a ax −
− − , a > 0; 3 3 − < < a a x Find the values of each of the following:
Question 11:–1 –1 1 tan 2cos 2sin 2
Question 12:cot (tan–1a + cot–1a)
Question 13:2 –1 –1 2 2 1 2 1 tan sin cos 2 1 1 x y x y − + + + , | x | < 1, y > 0 and xy < 1
Question 14:If sin –1 1 –1 sin cos 1 5 x
+ = , then find the value of x
Question 15:If –1 1 –1 1 tan tan 2 2 4 x x x x − + p + = − + , then find the value of x Find the values of each of the expressions in Exercises 16 to 18
Question 16:–1 2 sin sin 3
π
Question 17:–1 3 tan tan 4
π
Question 18:–1 3 –1 3 tan sin cot 5 2
+
Question 19:1 7 cos cos is equal to 6 − π (A) 7 6 p (B) 5 6 p (C) 3 p (D) 6 p
Question 20:1 1 sin sin ( ) 3 2
π − − − is equal to (A) 1 2 (B) 1 3 (C) 1 4 (D) 1
Question 21:1 1 tan 3 cot ( 3) − − − − is equal to (A) π (B) 2 p − (C) 0 (D) 2 3
