Question

If sec theta + tan theta =p then find cosec theta.

Answer 1

given,

Sec + tan = p

$\frac{1}{cos} + \frac{sin}{cos} = \frac{1 + sin}{cos} = \frac{p}{1}$


1 + sin =p

sin = p-1

cosec =
$\frac{1}{p - 1}$




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Answer 2

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

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