Chapter 2 Inverse Trigonometric Functions



Chapter 2 Inverse Trigonometric Functions1 Mark Questions Q1. Find the value of tan (cos–14/5 + tan–12/3) Q2. If we consider only the Principal value of the inverse trigonometric functions, then find the value of tan (cos-1152- sin-1417).Q3. If tan-1ax+tan-1bx=π2 , then find the value of x .Q4. If (a < 0) and x ?(– a, a), simplify tan-1xa2-x2 Q5. If x + y + z = xyz, then the value of tan-1x+tan-1y+tan-1z.Q6. Find the value of tan12cos-153 . Q7. If sin-135=x , find the value of cosx . Q8. Find the principal value of cos-132 . Q9. If sin-1x=y , then what will be the range of y? Q10. Show that sin-12x1-x2=2sin-1x. Q11. Find the value of cos-1cos13π6 . Q12. Find the value of tan-1211+tan-1724 . Q13. Find the value of tan-13a2x- x3a3- 3ax2 . Q14. Express 2tan-1x=… in terms of Sine and cosine.Q15. Write down the domain and Range of tan-1x . 4 Marks QuestionsQ1. Solve of the equation tan–1(x – 1) + tan–1x + tan–1(x + 1) = tan–1(3x) Q2. Solve of the equation sin-16x+sin-163x= - π2 . Q3. Find the value of sin2tan-113+costan-122 . Q4. Ifsin-11x= sin-11a+ sin-11b , then find the value of x .Q5. Evaluate: cos-1x+cos-1x2+ 123-3x2 when 12 ≤x≤1 . Q6. Find the value of cos2cos-1x+ sin-1x at x= 15 . Q7. What is the +ive integral solution of tan-1x+cos-1y1+ y2=sin-1310 ? Q8. Find value of cos-1cos2cot-12- 1 . Q9. If α=sin-132+ sin-113 and β=cos-132+ cos-113, then find whether α >βQ10. If sin-11-x=2sin-1x+π2 , then solve for x.Q11. Find the value of x satisfying the equation: tan-112+3- tan-11x= tan-113 .Q12. Find the solution of equation sin-1x+ sin-12x=π3 .Q13. Write the Simplified form of tanπ4+ 12cos-1ab+tanπ4- 12cos-1ab= ab Q14. Evaluate sin-1cotsin-12- 34+ cos-1124+sec-12 Q15. Find the value of tanπ4+ 12cos-1x+tanπ4- 12cos-1x, x≠0?6 Marks QuestionsQ1. Express tan-1cosx1- sinx, -π2<x<π2 in the simplest form.Q2. Prove that tan-11+x – 1 - x1+x+ 1 - x= π4-12 cos-1x . Q3. Solve tan-12x+ tan-13x= π4 . Q4.Show that sin-11213+cos-145+ tan-16316= π . Q5. Find the value of: tan12 sin-12x1+ x2+ cos-11- y2 1+ y2, x<1, y>0 and xy>1.Q6. Prove that 2 tan-1{tanα/2tan(π/4-β/2)}= tan-1{sin αcos β/(sin β+ cos α}Answers: Inverse Trigonometric Functions1 Marks QuestionsQ1. 176Q2. 329Q3. Q4. - sin-1xa Q5.Q6. 3- 52 Q8. π6 Q9. – π/2 ≤y ≤ π/2Q11. π/6Q12. tan-1 ?Q13. 3 tan -1 (x/a)4 Marks QuestionsQ1. x = 0Q2. - 112 Q3. 1415 Q4. aba2- 1 + b2 - 1 Q5. π3Q6. - 265 Q7. for x = 1, y = 2 and for x = 2, y = 7Q8. 3π4 Q9. α<β Q10.x = 0 Q11.x = 2 Q12. 2114 Q13. 2ba Q14. 0 Q15. 2x 6 Marks Questions Q1. x2+ π4 Q3. x= 16 Q5. x+y1-xy ................
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