Question

prove that 1/tan theta + cot theta - 1/1 + sin theta + 1/1 - sin theta = 2 sec square theta

Answer 1

Hello friend,

instead of theta i am using ' a ' okay! 

= sin a (1 + tan a ) + cos a (1+ cot a) 
= sin a(1+sin a /cos a ) +cos a(1+ cos a /sin a) 
= sin a (cos a +sin a )cos a + cos a (sin a +cos a)/sin a 

taking (cos a + sin a) common 

= (sin a /cos a +cos a / sin a)(cos a + sin a ) 
= (sin^2 a +cos^2 a)(cos a+ sin a )/sin a . cos a 

by using sin^2 a +cos^2 a =1 , 

= (cos a +sin a)/ sin a .cos a 
= cos a/sin a.cos a + sin a /cos a. sin a 
= 1/sin a +1/ cos a 
= cosec a +sec a