If sectheta + tantheta = p, then find the value of cosectheta
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Sec2θ - tan2θ = 1
(secθ + tanθ)( secθ - tanθ) = 1
p( secθ - tanθ) = 1
( secθ - tanθ) = 1/p and, ......-(1)
( secθ + tanθ) = p ..... - (2)
(1) + (2),
secθ = 1/2 (p + 1/p) ,
(2) - (1)
tanθ = 1/2 (p-1/p)
secθ / tanθ = cosecθ
Hence,
cosecθ = p +1/p / p-1/p = p2 +1 / p2 -1
(secθ + tanθ)( secθ - tanθ) = 1
p( secθ - tanθ) = 1
( secθ - tanθ) = 1/p and, ......-(1)
( secθ + tanθ) = p ..... - (2)
(1) + (2),
secθ = 1/2 (p + 1/p) ,
(2) - (1)
tanθ = 1/2 (p-1/p)
secθ / tanθ = cosecθ
Hence,
cosecθ = p +1/p / p-1/p = p2 +1 / p2 -1
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