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Prove cos^2x tanx / sinx = cosx?

1 Answer

Mar 28, 2018

We seek to prove that:

${cos}^{2} x \frac{tan x}{sin x} \equiv cos x$ $cos^2x tanx/sinx -= cos x$

Consider the LHS of the expression:

$L H S \equiv {cos}^{2} x \frac{tan x}{sin x}$ $LHS -= cos^2x tanx/sinx$

$\ \ \ \ \ \ \ \ = cos x * cosx * ((sinx/cosx)) / sin x$

$\ \ \ \ \ \ \ \ = cos x * cosx * (sinx/cosx) * 1/ sin x$

After cancelling we get:

$LHS = cos x * cancel(cosx) * (cancel(sinx)/cancel(cosx)) * 1/ cancel(sin x)$

$\ \ \ \ \ \ \ \ = cos x$

$\ \ \ \ \ \ \ \ = RHS \ \ \ QED$

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