How do you prove $(1-csc^2t)/ csc^2t = -1/sec^2t$ ?

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How do you prove $(1-csc^2t)/ csc^2t = -1/sec^2t$ ?

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Answer 1 · 2016-05-24T02:14:45

Prove trig expression.

Explanation:

Left side of the equation:
$(1 - 1/sin^2 t)/(1/sin^2 t) = (1 - sin^2 t)/sin^2 t (sin^2 t) = - cos^2 t$ .
$(- cos^2 t)$ can be written as : $- 1/(1/cos^2t) = - 1/(sec^2 t)$ .
Therefor:
$(1 - csc^2 t)/(csc^2 t) = - 1/(sec^2 t)$

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How do you prove $(1-csc^2t)/ csc^2t = -1/sec^2t$ ?

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How do you prove (1-csc^2t)/ csc^2t = -1/sec^2t(1-csc^2t)/ csc^2t = -1/sec^2t?

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How do you prove $(1-csc^2t)/ csc^2t = -1/sec^2t$ ?