if sec theta+tan theta = p,than prove that sin theta= p²-1/p²+1
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Step-by-step explanation:
p
2
−1
=
(secθ+tanθ)
2
+1
(secθ+tanθ)
2
−1
sec
2
θ+tan
2
θ+2secθtanθ+1
sec
2
θ+tan
2
θ+2secθtanθ−1
=
sec
2
θ+(tan
2
θ+1)+2secθtanθ
(sec
2
θ−1)+tan
2
θ+2secθtanθ
=
sec
2
θ+sec
2
θ+2secθtanθ
tan
2
θ+tan
2
θ+2secθtanθ
=
2sec
2
θ+2secθtanθ
2tan
2
θ+2secθtanθ
=
2secθ(secθ+tanθ)
2tanθ(tanθ+secθ)
=
2secθ
2tanθ
=tanθ×cosθ
=
cosθ
sinθ
×cosθ
=sinθ
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