How do you verify csc^2xcot^2x+csc^2x=csc^4x ?

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Answer 1 · 2018-03-05T12:33:21

Take $csc^2(x)$ common then it becomes:

$csc^2(x)$ (1+ $cot^2(x)$ )

which is equal to $csc^4(x)$

Basic trigonometric identities
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To prove $(csc^2x cot^2x + csc^2 x) = csc^4 x$

Taking common term $csc^2 x$ on L H S out,

$=> csc^2 x ( 1 + cot^2 x)$

But $csc^2 x = 1 + cot^2 x$ (Trigonometric identity.)

Hence $=> csc^2 x * csc^2 x = csc^4 x = R H S$

Q E D.

Answer 2 · 2018-03-05T13:29:47

It is given that, $csc^2xcot^2x+csc^2x=csc^4x$

$LHS=>1/sin^2x* cos^2x/sin^2x + 1/sin^2x$

$cos^2x/sin^4x + sin^2x/sin^4x$

$(cos^2x + sin^2x)/sin^4x$

$1/sin^4x = csc^4x$ ; [as we know $color(red)(sin^2x + cos^2x = 1$ ]