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

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

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

Answer»

(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