Question

Prove that:
Sec^2 x+cosec^2 x >=4

Answer 1

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