Question 969980
LHS.
={{{(cot^2(A)+sec^2(A))/(tan^2(A)+cosec^2(A))}}}
.
={{{(cos^2(A)/sin^2(A)+1/cos^2(A))/(sin^2(A)/cos^2(A)+1/sin^2(A))}}}
.
={{{(cos^4(A)+sin^2(A))/(sin^4(A)+cos^2(A))}}}
.
={{{((1-sin^2(A))^2+sin^2(A))/(sin^4(A)+cos^2(A))}}}
.
={{{(1+sin^4(A)-sin^2(A))/(sin^4(A)+cos^2(A))}}}
.
={{{(sin^4(A)+cos^2(A))/(sin^4(A)+cos^2(A))}}}
.
={{{1}}}
.
={{{sin^2(A)+cos^2(A)}}}
.
={{{sin(A)cos(A)*(sin(A)/cos(A)+cos(A)/sin(A))}}}(Taking out sinAcosA as common)
.
={{{sin(A)cos(A)*(tan(A)+cot(A))}}}
= RHS.