Log in to add a comment

## Answers

= 1 + cot a - cosec a + tan a + 1 - sec a + sec a + cosec a - sec a.cosec a

= 2 + cot a + tan a - sec a . cosec a

= 2 + (cos a)/(sin a) + (sin a)/(cos a) - sec a . cosec a

= 2 + (cos² a + sin² a)/(sin a. cos a) - sec a . cosec a

= 2 + sec a . cosec a - sec a . cosec a

= 2

__proved__

*(1 + tan a + sec a )(1+ cot a - cosec a)*

*1 + cot a - cosec a + tan a + tan a.cot a - tan a.cosec a + sec a + sec a.cot a - sec a.cosec a*

*[ cosec a get cancelled by - cosec a ]*

*[tan a = 1/tan a and get cancelled and become 1]*

*[tan a = sin a / cos a and its reciprocal become sec a / cosec a ]*

*[cot a = cos a / sin a and its reciprocal becomes cosec a / seca]*

*1 + cot a - cosec a + tan a + 1 - sec a + sec a + cosec a - sec a.cosec a*

*2 + (cos a)/(sin a) + (sin a)/(cos a) - sec a . cosec a*

*2 + (cos² a + sin² a)/(sin a. cos a) - sec a . cosec a*

*2 + sec a . cosec a - sec a . cosec a*

*2.*

*Hence proved*