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12th Standard English Medium Maths Subject Inverse Trigonometric Functions Creative 5 Mark Questions with Solution

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. Find the domain of the following functions
    (i) f(x) = sin-1(2x - 3)
    (ii) f(x) = sin-1x + cos x

  2. Write the function \(f(x)=\tan ^{-1} \sqrt{\frac{a-x}{a+x}}-a<x<a \) in the simplest form

  3. Simplify \({ sin }^{ -1 }\left( \frac { sinx+cosx }{ \sqrt { 2 } } \right) ,\frac { \pi }{ 4 }\) 

  4. If \({ tan }^{ -1 }\left( \frac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right) =a\) than prove that x= sin 2a

  5. Prove that \({ tan }^{ -1 }\left( \frac { 1-x }{ 1+x } \right) -{ tan }^{ -1 }\left( \frac { 1-y }{ 1+y } \right) ={ sin }^{ -1 }\left( \frac { y-x }{ \sqrt { 1+{ x }^{ 2 } } .\sqrt { 1+{ y }^{ 2 } } } \right)\)

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