Question

if theta = 45° then sec theta cot theta - cosec theta tan theta is​

Answer 1

Answer:

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