Saturday, 4 May 2013

INVERSE TRIGONOMETRIC FUNCTIONS


S.NO. INVERSE TRIGONOMETRIC FUNCTIONS
EXERCISE 2.1
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

3 comments:

  1. pls solve exer2.2 also please

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  2. You can see Solution of exercise 2.2 with in 48 hour
    thanks

    ReplyDelete
  3. plz solve miscellaneous also plzzzzzzzzzz

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