show that sec^2x+cosec
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Answer:
Given,
sec
2
x+csc
2
x
=1+tan
2
x+1+cot
2
x
=2+tan
2
x+cot
2
x
we know that, AM>GM
2
tan
2
x+cot
2
x
>
tan
2
xcot
2
x
tan
2
x+cot
2
x>2
tan
2
x+cot
2
x+2>2+2
tan
2
x+cot
2
x+2>4
1+tan
2
x+1+cot
2
x>4
sec
2
x+csc
2
x>4
Hence proved.