Question

1/cosec A -cot A-1/sin A=1/sin A -1/cosecA+cotA ,Prove it by using trigonometric identities.

Answer 1

LHS = 1/(cosecA - cotA) - 1/sinA

we know, cosec²A - cot²A = 1......(i)

= (cosec²A - cot²A)/(cosecA - cotA) - 1/sinA [from equation (i), ]

= (cosecA - cotA)(cosecA + cotA)/(cosecA - cotA) - 1/sinA

= (cosecA + cotA) - 1/sinA

= cosecA + cotA - cosecA [ as 1/sinA = cosecA]

= cotA

= cosecA - (cosecA - cotA)/1

= cosecA - (cosecA - cotA)/(cosec²A - cotA)

= 1/sinA - (cosecA - cotA)/(cosecA - cotA)(cosecA + cotA)

= 1/sinA - 1/(cosecA + cotA) = RHS

Answer 2

Answer:

At the 9th step it is cosec ^2-cot^2

Everything is ok but it is little mistake.

Step-by-step explanation: