Question

Prove the trigonometric identity sin⁡A/1−cos⁡ A =cosec⁡ A+ cot⁡A​

Answer 1

Step-by-step explanation:

[ cos a = cot a / cosec a ]

sin a / 1 - cot a / cosec a

sin a / cosec a - cot a / cosecA

[ sin a = 1 / cosec a ]

1 / cosec a / cosec a - cot a / cosec a

{ neglect cosec a }

1 / cosec a - cot a

multiply and divide by cosec a + cot a

1 / (cosec a - cot a) × (cosec a + cot a) / (cosec a + cot a)

{ (a-b) (a+b) = a² - b² }

{ (cosec a - cot a) (cosec a + cot a) = cosec²a - cot²a }

cosec a + cot a / cosec²a - cot²a

[ cosec²a - cot²a = 1 ]

cosec a + cot a / 1

cosec a + cot a ✔️

hence proved.