Question

If `sec theta + tan theta = p`, prove that
(i)` sec theta =(1)/(2)(p+(1)/(p)) " (ii) "tan theta =(1)/(2)(p-(1)/(p)) " (iii) " sin theta =(p^(2)-1)/(p^(2)+1).`

Answer 1

`sectheta+tantheta=p." " `...(i)
`sec^(2)theta -tan^(2)theta=1. " " `...(ii)
On dividing (ii) by (i), we get
`sec theta-tantheta=(1)/(p)." " ` ...(iii)
`therefore " from (i) and (iii), we get " sectheta=(1)/(2)(p+(1)/(2)),tantheta=(1)/(2)(p-(1)/(p)). `
Also, ` sintheta=(tantheta)/(sectheta)=((1)/(2) (p-(1)/(p)))/((1)/(2)(p+(1)/(p)))=((p^(2)-1))/((p^(2)+1)).`