Question

prove that
sec^2x+cosec^2x>4

Answer 1

hey there !!

sec^2x = 1+tan^2 x

cosec^2x = 1+ cot^2x

so according to question,

sec^2x + cosec^2x = 2 + tan^2x+cot^2x


but , we know that A.M > G.M

so , (tan^2x + cot^2x)/2 >√(tan^2x.cot^2x)

=) tan^2x + cot^2x > 2 ×1

=) tan^2x + cot^2x >2

now ,

adding 2 on both sides , we get

(1 +tan^2x) + (1+cot^2x)> 2 + 2


=) sec^2x + cosec^2x >4

hence proved