Question

prove cotA+cosecA-1 / cotA-cosecA+1 = 1+cosA/sinA​

Answer 1

Answer:

=cot A + cosecA - 1/cotA-cosec A+1=1+cos A/sin A

=first put the value of 1 in the numerator in terms of cosec^2 -cot^2=1.

so,

=cotA + cosec A -(cosec^2 A -cot^2)/

cotA-cosecA+1.

now take the common in the numerator

=cotA+cosec -(1 +cotA - cosecA)/1+cotA-cosecA.

= cotA+cosecA.

= cosA/sinA+ 1/sinA

so,

cosA+1/sinA=cosA+sinA .

hence proved