Question

If sec θ + tan θ = p , then how do I show that sin θ = (p^2 - 1) / (p^2 + 1)?

Answer 1

see the images attached!

hope it helps! 

Answer 2

Put the value of P in equation......
(sec @ +tan@)2-1/(sec @ +tan@)2+1
sec2@+tan2@+2sec@tan@-1/sec2@+tan2@+2sec@tan@+1


sec2@+tan2@+2sec@tan@-(sec2@-tan2@)/
sec2@+tan2@+2sec@tan@+sec2@-tan2@

sec2@+tan2@+2sec@tan@-sec2@+tan2@
sec2@+tan2@+2sec@tan@+sec2@-tan2@

2tan2@+2sec@tan@/2sec2@+2sec@tan@


2tan@(tan@+sec@)/2sec@(sec@+tan@)

2tan@/2sec@
2sin@/cos@/2/cos@

...sin@ hence proved Q.E.D