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^{1}x= y, then  
14  tan^{1}√ 3 − sec^{1} (− 2) is equal to  
EXERCISE 2.2


1  Prove the following: 3sin^{1}x = sin^{1}(3x4x^{3}), x∈[1/2,1/2]  
2  Prove the following: 3cos^{1}x = cos^{1}(4x^{3}3x), x∈[1/2,1]  
3  prove that tan^{1}2/11 + tan^{1}7/24 = tan^{1}1/2  
4  prove that 2tan^{1}1/2 + tan^{1}1/7 = tan^{1}31/17  
5  Write the following functions in the simplest form: tan1(√(1 + x2) 1) /x ,x ≠ 0  
6  Write the following functions in the simplest form: tan^{1}(1/√( x^{2}1) ,x >1  
7  Write the following functions in the simplest form: tan^{1}(√(1cosx)/(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/√(a^{2} x^{2}) , x < a  
10  Write the following functions in the simplest form: tan^{1}(3a^{2}x x^{3}/(a^{3} 3ax^{2}) , a >0 ;  
11  Find the values of each of the following: tan^{1}[2cos(2sin^{1}1/2)]  
12  Find the values of cot(tan^{1}a +cot^{1}a)  
13  tan1/2[sin^{1} 2x/(1+x^{2})+cos ^{1}(1y^{2})/(1+y^{2})],  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} (x1)/(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^{1}3/2)  
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^{1}8/17 + sin^{1}3/5 = tan^{1}77/36  
5  Prove that cos^{1}4/5 + cos^{1}12/13 = tan^{1}33/65  
6  Prove that cos^{1}12/13 + sin^{1}3/5 = sin^{1}56/65  
7  Prove that tan^{1}33/65 = sin^{1}5/13 + cos^{1}3/5  
8  Prove that tan^{1}1/5 + tan^{1}1/7 +tan^{1}1/3 + tan^{1}1/8 = 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}(1x)/(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 
INVERSE TRIGONOMETRIC FUNCTIONS
Saturday, 4 May 2013
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pls solve exer2.2 also please
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