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Find the value of $x$ if \( sin \bigg ( sin^{-1} \frac{1}{5} + cos^{-1} \: x \bigg) = 1\).

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  • \( sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}\)
  • \( sin\large\frac{\pi}{2}=1\: or \: sin^{-1}1=\large\frac{\pi}{2}\)
Given $\; sin \bigg ( sin^{-1} \large\frac{1}{5} + cos^{-1} \: x \bigg) = 1$:
 
We know that $sin \large\frac{\pi}{2}=1 \Rightarrow$ the R.H.S of the equation $\:sin^{-1}\large\frac{1}{5}+cos^{-1}x$ should be =$\;\large\frac{\pi}{2}$
 
Given that $sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}$, if $sin^{-1}\large\frac{1}{5}+cos^{-1}x=\large\frac{\pi}{2} \Rightarrow x = \large\frac{\pi}{2}$

 

answered Feb 22, 2013 by thanvigandhi_1
edited Mar 15, 2013 by thanvigandhi_1
 
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