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## Saturday, 4 May 2013

### 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