Chapter 3 : MATHS : XII : Trigonometric Functions: Properties of Inverse Trigonometry : Test 5

Chapter #3: Properties of Inverse Trigonometry : Test 5
Marks -20                                                            Time - 40 Min

 

Q1)  Show that                                                                   (6M)

      a) 2tan^-1x = cos^-1(1-x²/1+x²) For x>=0
      b) 2tan^-1x =  tan^-1(2x/1-x²) For -1

Q2) Prove the following properties                                    (6M)

       a) sin^-1(x) + cos^-1(x) = π/2  for x∈[-1,1]

       b) tan^-1(x) + tan^-1(y) = tan^-1((x+y)/(1-xy)),
                                                    if x,y > 0 and xy<1 font="">

Q3) Prove the property                                                     (4M)

       a) cosec^-1(-x) = - cosec^-1(x)

       b) cot^-1(-x) = π - cot^-1(x)

Q4) Show that                                                                   (4M)

        tan^-1x + tan^-1(2x/1+x²) = tan^-1(3x - x³/1-3x²) 
                                                    for |x|<1 1="" br="">

Refer :Tricks and Formulae