Show that (1 + cot θ - cosec θ )(1 + tan θ + sec θ ) = 2.

24
If (a cos θ – b sin θ) = x and (a sin θ + b cos θ) = y, prove that a²+ b² = x² + y².
25
If x = p sec θ + q tan θ and y = p tan θ + q sec θ, provethat x² - y² = p² - q².
27
If cosec θ - sin θ = a, sec θ - cos θ = b, prove that a ²b ²(a ²+b ²+ 3) = 1.
28
Prove that (sin θ + sec θ) ²+ (cos θ + cosec θ) ²=(1 + sec θ cosec θ) ².