Question

Any plz help me to solve this question. Plzz...

Answer 1

Numerator = tan theta + sec theta -1 
= sin theta/cos theta + 1/cos theta - 1 
= (sin theta + 1)/cos theta -1 

denominator = (sin theta -1)/cos theta +1 

multiply both by cos theta 

numerator = sin theta +1 - cos theta 
= 2 sin theta/2 cos theta/2 + 2 sin^ theta/2 

denominator = 2 sin theta/2 cos theta/2 - 2 sin ^2 theta/2 

divide 

number = (cos theta/2 + sin theta/2)/(cos theta/2 - sin theta/2) 

= (cos theta/2 + sin theta/2)^2/(cos^2 theta/2- sin ^2 theta/2) 
= (cos^2 theta/2+ sin^2 theta/2 + 2 cos theta/2 sin theta/2)/(cos theta) 
= (1+ sin theta)/ cos theta

= sec theta+ tan theta

 

Answer 2

sintheta/costheta+costheta/costheta by sintheta/costheta-1/costheta+1
sintheta+1/costheta by sintheta-1+costheta/costheta
sintheta+1/costheta×costheta/sintheta-1
=1+sintheta/costheta