Question

${\csc }^{6}A-{\cot }^{6}A=3{\cot }^{2}A{\csc }^{2}A+1$

Answer 1

${cosec}^{6}A-{cot}^{6}A=3{cot}^{2}A\ast {cosec}^{2}A+1$

${cosec}^2\theta -{cot}^2\theta =1(\frac{6}{2}=3)$

$3\ast 1=3{cot}^{2}A\ast {cosec}^{2}A+1$

$3\ast 1=\frac{3}{{sec}^2(90-A)}\ast {sec}^2(90-A)+1$

$3=3\ast 1$

$3=3$

Hence proved