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Tan A +cot A
sinA/cosA +cos A/sin A
on taking LCM
(Sin²A+cos²A)/sinA cos A
As we know sin²A+cos²A=1
1/sinA cosA⇒cosecA secA                          {1/cosA=secA, 1/sinA=cosecA}
Hence proved.........................
1 4 1

tan A + cot A=sec A cosec A

LHS=tan A +cot A

       =sin A/cos A+ cos A/sin A

      =(sin^2 A+cos^2 A)/cos A sin A

      =1/cos A sin A

      =sec A cosec A


Hope it helps!

3 4 3
tan A +cot A
sinA/cosA +cos A/sin A
taking LCM
(Sin²A+cos²A)/sinA cos A
1/sinA cosA⇒cosecA secA
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