Question

If 2sin theta - 1=0,then prove that sec theta +tan theta =root 3

Answer 1

sin theta = 1/2 ,(from given condition)

so, cos theta = √1-(1/2)^2

= √3/2

sec theta =1/cos theta

tan theta = sin theta /cos theta

proof:-

LHS

sec theta +tan theta = 1/cos theta + sin theta /cos theta

= (1+sin theta)/cos theta

put sin theta = 1/2 and cos theta = √3/2

now sec theta + tan theta = (1+1/2)/(√3/2)

= 3/√3

= √3= RHS