Question

Prove that: (sin - sec)2 + (cos- cosec)2 = (1- seccosec)2

Answer 1

Answer:

Step-by-step explanation:

Here is ur answer

(sin A + sec A)² + (Cos A + Cosec A)²

= Sin² A + sec² A + 2 Sin A Sec A + Cos² A + Cosec² A + 2 Cos A Cosec A

= Sin²A + COs²A + Sec²A + Cosec²A + 2 Sin A SecA + 2 Cos A Cosec A

= 1  +  [ 1/Cos²A + 1/ Sin²A ] +  [ 2 Sin A / Cos A + 2 Cos A / SIn A ]

= 1 + (Sin²A + COs²A)/ [Cos²A Sin²A ]  + 2 [ SIn² A + Cos²A ] / [ SinA CosA

= 1 + 1/Cos²A 1/Sin²A  + 2 1/SinA  1/CosA

= 1 + Sec²A Cosec²A + 2 COsecA Sec A

= (1 + SecA CosecA )²