Question

cos(90-A) sec(90-A)tanA/ cosec(90-A) sin(90-A) cot(90-A)+ tan(90-A)/ cot A=2

Answer 1

lhs = cos(90-A)sec(90-A)tanA/cosec(90-A)sin(90-A)cot(90-A) + tan(90-A)/cotA

= sinAcosecAtanA /secAcosAtanA  + cotA /cotA
=tanA/tanA + cotA/cotA
=1+1
= 2
=rhs

here we used cos (90-A) = sinA
sec(90-A) = cosecA
cosec(90-A) =secA
sin(90-A) =cos A
cot(90-A) =tan A

tan(90-A) = cotA
sinAcosecA =1
cosAsecA =1

Answer 2

Cos(90-A)sec(90-A)tan A/cosec(90-A)sin(90-A)cot(90-A)+tan(90-A)/cot A

= cos A cosec A tan A/cosec A cos A tan A +cot A/cot A

Everything cancels and we are left with

= 1×1×1/1×1×1 + 1/1

=1/1 + 1/1

= 1 + 1

=2