Question

prove cotA + cosecA - 1 / cotA - cosecA + 1 = cosecA + cotA

Answer 1

refer to the attachment

Answer 2

Step-by-step explanation:

To prove,

(cot A + cosec A -1) = (1+cos A)

(cot A - cosec A +1) sin A

LHS= cos A + 1 - sin A

sin A sin A sin A

cos A - 1 + sin A

sin A sin A sin A

= (cos A + 1 - sin A) × (cos A + 1 - sin A)

(cos A - 1 + sin A) (cos A + 1 - sin A)

= (cos A + 1 - sin A) (cos A + 1 - sin A)

(cos A - 1 + sin A) (cos A + 1 - sin A)

= (cos A + 1 - sin A)^2

cos^2 A - (1 - sin A)^2

= (cos^2 A - 2 cos A (1 - sin A) + (1 - sin A)^2)

(cos^2 A - 1 + 2 sin A - sin^2 A)

= cos^2 A-2cosA+2 sinA cosA +1-2 sinA + sin^2 A

1 - sin^2 A - 1 + 2 sin A - sin^2 A

= (2 - 2 cos A + 2 sin A cos A - 2 sin A)

(2 sin A - 2 sin^2 A)

= 2 (1 - cos A) (1 - sin A)

(2 sin A (1 - sin A) )

= 1 - cos A

sin A

= RHS