Question

who can solve this matter


cot a+coseca-1/cot a-cosec +1 =1+cos a/sin a​

Answer 1

Question:

Prove that,

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

Solution:

LHS

=> (cot(A) + cosec(A) - 1)/(cot(A) - cosec(A) + 1)

=> [(cosec(A) + cot(A) - 1)(cosec(A) - cot(A))] / [(cot(A) - cosec(A) + 1)(cosec(A) - cot(A))]

=> (cosec²(A) - cot²(A) - cosec(A) + cot(A))/ [(cot(A) - cosec(A) + 1)(cosec(A) - cot(A))]

=> (1 - cosec(A) + cot(A))/ [(cot(A) - cosec(A) + 1)(cosec(A) - cot(A))]

=> (cot (A) - cosec(A) + 1)/ [(cot(A) - cosec(A) + 1)(cosec(A) - cot(A))]

=> 1/(cosec(A) - cot(A))

=> (cosec(A) + cot(A)) / [(cosec(A) - cot(A))(cosec(A) + cot(A))]

=> (cosec(A) + cot(A)) / (cosec²(A) - cot²(A))

=> cosec(A) + cot (A)

=> (1/sin(A)) + (cos(A)/sin(A))

=> (1 + cos(A))/sin(A)

=> RHS

Hence Proved!

Answer 2

Answer:

Refer to the Attachment.

Hope it Helps !!!!!