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CBSE 12 Math Practice Paper 02

CBSE 12 Math Practice Paper 02 - Coding Bihar

CBSE 12 Math Practice Paper

CBSE 12 Math Practice Paper 02

1. Find the principal values of
      (i)  \(sin^{-1}\frac{1}{\sqrt2}\)
      (ii) \(sin^{-1}\big(\frac{-1}{2}\big)\)
      (iii) \(cos^{-1}\big(\frac{-1}{2}\big)\)

2. Find the values of the following
     (i) \(tan^{-1}(1)+ cos^{-1}(\frac{-1}{2})+sin^{-1}(\frac{-1}{2})\)
     (ii) \(cos^{-1}\frac{1}{2}+sin^{-1}({1}{2})\)
     (iii) \(cos^{-1}(cos\frac{13\pi}{6})\)

3. Show that 
   (i) \(Sin^{-1}(2x\sqrt{1-x^2})=\)\(2sin^{-1}x, \frac{-1}{\sqrt2}\leq x \leq \frac{1}{\sqrt2}\)
   (ii) \(Sin^{-1}(2x\sqrt{1-x^2})=2cos^{-1}x,\)\( \frac{1}{\sqrt2}\leq x \leq 1\)
   (iii) \(Sin^{-1}\frac{3}{5}-sin^{-1}\frac{8}{17}=\)\(cos^{-1}\frac{84}{85}\)

4. Prove the following:
    (i)\(tan^{-1}\frac{2}{11} + tan^{-1}\frac{1}{7}= tan^{-1}\frac{1}{2}\)
    (ii)\(2tan^{-1}{\frac{1}{2}} + tan^{-1}{\frac{1}{7}}=tan^{-1}{\frac{31}{17}}\)

 Sandeep Gupta

Posted by Sandeep Gupta

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