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Home / Doubts and Solutions/ICSE/Class 11 Science/Mathematics

If tan x=k , then find the value of fraction numerator sin x over denominator cos cubed x end fraction plus fraction numerator cos begin display style x end style over denominator begin display style sin cubed end style begin display style x end style end fraction

 

 

Asked by SanskarAgarwal86 6th August 2018, 10:25 PM
Answered by Expert
Answer:
begin mathsize 16px style fraction numerator sinx over denominator cos cubed straight x end fraction plus fraction numerator cos begin display style straight x end style over denominator begin display style sin cubed end style begin display style straight x end style end fraction equals fraction numerator sin begin display style straight x end style over denominator cos begin display style straight x end style end fraction cross times fraction numerator 1 over denominator begin display style cos squared end style begin display style straight x end style end fraction plus fraction numerator cos begin display style straight x end style over denominator sin begin display style straight x end style end fraction cross times fraction numerator 1 over denominator begin display style sin squared end style begin display style straight x end style end fraction equals tanx cross times sec squared straight x plus cotx cross times cosec squared straight x equals tanx cross times open parentheses 1 plus tan squared straight x close parentheses plus fraction numerator 1 over denominator tan begin display style straight x end style end fraction cross times open parentheses 1 plus cot squared straight x close parentheses equals tanx cross times open parentheses 1 plus tan squared straight x close parentheses plus fraction numerator begin display style 1 end style over denominator begin display style tan straight x end style end fraction cross times open parentheses 1 plus fraction numerator 1 over denominator tan squared straight x end fraction close parentheses equals straight k cross times open parentheses 1 plus straight k squared close parentheses plus 1 over straight k cross times open parentheses 1 plus fraction numerator begin display style 1 end style over denominator begin display style straight k squared end style end fraction close parentheses Simplifying space this space we space get equals fraction numerator open parentheses straight k squared plus 1 close parentheses begin display style open parentheses straight k to the power of 4 plus 1 close parentheses end style over denominator straight k cubed end fraction end style
Answered by Expert 7th August 2018, 9:53 AM
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