Try to prove the inequality by analysis: (1 + 1 / sin ^ a) (1 + 1 / cos ^ a) > = 9

Try to prove the inequality by analysis: (1 + 1 / sin ^ a) (1 + 1 / cos ^ a) > = 9

(1+1/sin^a)(1+1/cos^a)
=1+1/sina^2+1/cosa^2+1/(sinacosa)^2
=1+(sina^2+cosa^2)/(sinacosa)^2+1/(sinacosa)^2
=1+2/(1/2sin2a)^2
=1+8/sin2a^2
Because sin2a = 1 + 8 / 1 = 9
So: (1 + 1 / sin ^ a) (1 + 1 / cos ^ a) > = 9