INVERSE TRIGONOMETRIC FUNCTIONS

S.NO.	INVERSE TRIGONOMETRIC FUNCTIONS
	EXERCISE 2.1
1	Find the principal values of the following: sin-1(-1/2)
2	Find the principal value of cos-1(√3/2)
3	Find the principal value of cosec-1 (2)
4	Find the principal value of tan-1 (-√3)
5	Find the principal value of cos-1(-1/2)
6	Find the principal value of tan-1(-1)
7	Find the principal value of sec-1(2/√3)
8	Find the principal value of cot-1(√3)
9	Find the principal value of cos-1(-1/√2)
10	Find the principal value of cosec -1(-√2)
11	Find the values of the following: tan-1(1) + cos-1(-1/2) +sin-1(-1/2)
12	Find the values of the cos-1(1/2) + 2sin-1(1/2)
13	if sin-1x= y, then
14	tan-1√ 3 − sec-1 (− 2) is equal to
	EXERCISE 2.2
1	Prove the following: 3sin-1x = sin-1(3x-4x3), x∈[-1/2,1/2]
2	Prove the following: 3cos-1x = cos-1(4x3-3x), x∈[-1/2,1]
3	prove that tan-12/11 + tan-17/24 = tan-11/2
4	prove that 2tan-11/2 + tan-11/7 = tan-131/17
5	Write the following functions in the simplest form: tan-1(√(1 + x2) -1) /x ,x ≠ 0
6	Write the following functions in the simplest form: tan-1(1/√( x2-1) ,|x| >1
7	Write the following functions in the simplest form: tan-1(√(1-cosx)/(1+cos x ) ,|x| < pi
8	Write the following functions in the simplest form: tan-1((cos x -sin x )/(cosx + sinx ) ,|x| < pi
9	Write the following functions in the simplest form: tan-1(x/√(a2- x2) , |x| < a
10	Write the following functions in the simplest form: tan-1(3a2x -x3/(a3- 3ax2) , a >0 ;
11	Find the values of each of the following: tan-1[2cos(2sin-11/2)]
12	Find the values of cot(tan-1a +cot-1a)
13	tan1/2[sin-1 2x/(1+x2)+cos -1(1-y2)/(1+y2)], | x | < 1, y > 0 and xy < 1
14	if sin(sin-1 1/5 + cos-1 x)=1 , then find the value of x
15	If tan-1 (x-1)/(x+1) + tan-1(x+1)/(x+2) = π/4, then find the value of x
16	Find the values of each of the expressions sin-1(sin 2π/3)
17	Find the values of each of the expressions tan-1(tan 3π/4)
18	Find the values of each of the expressions tan(sin-1 3/5 + cot-13/2)
19	Find the values of each of the expressions cos-1(cos 7π/6) is equal to
20	sin (π/3 - sin-1(-1/2) is equal to
21	tan-1√3 -cot-1(-√3 ) is equal to
	Miscellaneous Exercise on Chapter 2
1	Find the value of the following: cos-1(cos 13π/6)
2	Find the value of the following: tan-1(tan 7π/6)
3	Prove that 2sin-1 3/5 = tan-1 24/7
4	Prove that sin-18/17 + sin-13/5 = tan-177/36
5	Prove that cos-14/5 + cos-112/13 = tan-133/65
6	Prove that cos-112/13 + sin-13/5 = sin-156/65
7	Prove that tan-133/65 = sin-15/13 + cos-13/5
8	Prove that tan-11/5 + tan-11/7 +tan-11/3 + tan-11/8 = π/4
9	Prove that
10	prove that
11	prove that
12	prove that
13	Solve the following equations: 2tan-1 (cos x ) = tan -1(2cosec x )
14	Solve the equation tan-1(1-x)/(1+x) = 1/2 tan -1 x , (x>0)
15	sin (tan-1 x), | x | < 1 is equal to
16	sin-1(1 - x) - 2 sin-1 x = π/2, then x is equal to
17	tan -1(x/y) - tan-1( x- y)/(x+y) is equal to