Principle Of Mathematical Induction

Question
CBSEENMA11015500

The expression fraction numerator tan space straight A over denominator 1 minus cot space straight A end fraction plus space fraction numerator cot space straight A over denominator 1 minus space tan space straight A end fraction can be written as

  • sin A cos A+1

  • sec A cosec A+1

  • tan A + cot A

  • Sec A + cosec A

Solution

B.

sec A cosec A+1

Given expression is
fraction numerator tan space straight A space over denominator 1 minus cot space straight A end fraction space plus fraction numerator cot space straight A over denominator 1 minus space tan space straight A end fraction
space equals space fraction numerator sin begin display style space end style begin display style straight A end style begin display style space end style over denominator cos begin display style space end style begin display style straight A end style end fraction space straight x space fraction numerator Sin space straight A over denominator Sin space straight A space minus Cos space straight A end fraction
plus fraction numerator Cos space straight A over denominator Sin space straight A end fraction space straight x space fraction numerator Cos space straight A over denominator Cos space straight A minus space Sin space straight A end fraction
space equals space fraction numerator 1 over denominator Sin space straight A space minus Cos space straight A end fraction open curly brackets fraction numerator begin display style sin cubed end style begin display style space end style begin display style straight A end style begin display style space end style begin display style minus end style begin display style space end style begin display style begin display style Cos end style cubed end style begin display style space end style begin display style space end style begin display style straight A end style over denominator Cos space straight A space sin space straight A end fraction close curly brackets
space equals fraction numerator Sin squared space straight A space plus space sin space straight A space cos space straight A space plus space cos squared space straight A over denominator Sin space straight A minus space Cos space straight A space end fraction
equals space fraction numerator 1 plus space sin space straight A space cos space straight A over denominator sin begin display style space end style begin display style straight A end style begin display style space end style begin display style cos end style begin display style space end style begin display style straight A end style begin display style space end style end fraction
space equals space space 1 plus space sec space straight A space cosec space straight A space

Sponsor Area

Some More Questions From Principle of Mathematical Induction Chapter

Find 1 radian angle in degrees, minutes, seconds.