Find the principal value of tan-1(-1)
Saturday, May 4, 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 |
If sin-1x=y then
Question 13:
Answer: Here we can see that if sin-1x=y then y must be the principle value branch of the sine inverse so now we know that the principal value branch of the sine inverse is [-
/2,/2]so the correct answer is option (B).
/2,/2]so the correct answer is option (B).
Solve the equation using property of determinant
(Solve the equation using property of determinant)
5. Solve the equation
, a ≠ 0
Apply R1->R1+R2+R3 we get
Take 3x+a common from first row we get
Apply C2->C2-C1 and C3->C3-C1 we get
Open the expansion using first row we get
ð 3x+a= 0
3x = - a
x = - a/3
Answer x = -a/3
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