How do evaluate (1/cos^2 40) - (1/cot^2 40)?

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Answer 1 · 2018-04-25T14:09:14

$1$

We know that,

$color(blue)((1)1/cos^2theta=sec^2theta and 1/cot^2theta=tan^2theta$

$color(red)((2)sec^2theta-tan^2theta=1$

Let,

$X=1/cos^2 40-1/cot^2 40...tocolor(blue)(Apply(1))$

$X=sec^2 40-tan^2 40...tocolor(red)(Apply(2)$

$X=1$