XII. Show that cos[ tan-'{sin (cotx...
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XII. Show that cos[ tan-'{sin (cotx)]]= 1** v 2+x² LL show that x+y+z = XYZ

JEE/Engineering Exams
Maths
Solution
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cot ( ^{-1} ). (Make biangle) ( left.theta=cot ^{-1} x quad frac{sqrt{1+x^{2}}}{x}right} ) ( Rightarrow sin (Q) ) ( Rightarrow frac{1}{sqrt{1+x^{2}}} ) ( tan ^{-1} frac{1}{sqrt{1+x^{2}}} frac{sqrt{2+x^{2}}}{sqrt{1+x^{2}}} ) ( cos theta_{1} ) ( =frac{sqrt{1+x^{2}}}{sqrt{2+x^{2}}}=sqrt{frac{1+x^{2}}{2+x^{2}}}=operatorname{PHS} ) Flence Proved
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