if sec theta+tan theta =p ,prove that sin theta = (p square- 1) / (p square + 1) - Maths - Introduction to Trigonometry

Question

if sec theta+tan theta =p ,prove that sin theta = (p square- 1)
/ (p square + 1)

Vishal Rawat · Answer

= Taking R H S i e, (p2-1) / (p2+1)
= Putting value of p in given equation
= [(sec0+tan0)2-1] / [(sec0+tan0)2+1]
= (sec20+tan20+2sec0tan0-1) /
(sec20+tan20+2sec0tan0+1)
= (sec20-1)+tan20+2sec0tan0 /
(1+tan20)+sec20+2sec0tan0
= tan20+tan20+2sec0tan0 /
sec20+sec20+2sec0tan0 [ As
sec20-1=tan20
1+tan20=sec20 ]
= 2tan20+2sec0tan0 / 2sec20+2sec0tan0
= 2tan0+(tan0+sec0) / 2sec0+(sec0+tan0) [ Taking 2tan0 2sec0 as
common ]
= tan0 / sec0 [ 2 and tan0+sec0 gets cancelled above ]
= sin0/cos0 / 1/cos0 [ As
tan0=sin0/cos0 and sec0=1/cos0 ]
= sin0/1
= sin0
= L H S
Hence Proved