Question

Heya Guys...






Prove that sec²θcosec²θ - 2 - cot²θ = tan²θ?




Please answer it fast tomorrow is my exam!!!!

Answer 1

sec²θcosec²θ - 2 -cot²θ

= sec²θcosec²θ - 1 - 1 -cot²θ

= sec²θcosec²θ - 1 - (1 + cot²θ)

= sec²θcosec²θ -1 - cosec²θ          [ 1+ cot²A = cosec²A ]

= cosec²θ(sec²θ - 1) - 1

= cosec²θtan - 1                              [ 1 + tan²θ = sec²θ ]

= 1/sin²θ X sin²θ/cos²θ - 1              [ cosecA = 1/sinA ]

= 1/cos²θ - 1

= sec²θ - 1                                       [ secA = 1/cosA ]

= tan²θ                                             [ 1 + tan²A = sec²A ]

Hence, Proved