Question

Prove that: (sin θ – cosec θ)² + (cos θ – sec θ)² = cot² θ + tan² θ – 1

Answer 1

(sin θ – cosec θ)² + (cos θ – sec θ)² 

= sin² θ + cosec² θ – 2 sinθ . cosecθ . + cos² θ + sec² θ – 2 cosθ . sec θ 

= (sin² θ + cos² θ) + cosec² θ + sec² θ – 2 – 2 

= 1 + (1 + cot² θ) + (1 + tan² θ) – 2 – 2

= cot² θ + tan² θ + 3 – 4 

= cot² θ + tan² θ – 1