prove that tan-1 x = 2tan-1 {cosec(tan-1x) - tan (cot-1x)

Asked by poojaparmar065 | 27th Apr, 2014, 12:25: PM

Expert Answer:

tan to the power of minus 1 end exponent x equals 2 tan to the power of minus 1 end exponent open curly brackets cos e c open parentheses tan to the power of minus 1 end exponent x close parentheses minus tan open parentheses co t to the power of minus 1 end exponent x close parentheses close curly brackets   equals 2 tan to the power of minus 1 end exponent open curly brackets fraction numerator square root of 1 plus x squared end root over denominator x end fraction minus 1 over x close curly brackets  equals 2 tan to the power of minus 1 end exponent open curly brackets fraction numerator open parentheses square root of 1 plus x squared end root minus 1 close parentheses open parentheses square root of 1 plus x squared end root plus 1 close parentheses over denominator x open parentheses square root of 1 plus x squared end root plus 1 close parentheses end fraction close curly brackets  equals 2 tan to the power of minus 1 end exponent open curly brackets fraction numerator x over denominator 1 plus square root of 1 plus x squared end root end fraction close curly brackets  w h i c h space i s space a n space i d e n t i t y

Answered by  | 28th Apr, 2014, 09:23: AM

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