How do you verify $sinx + cosx cotx = cscx$ ?

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Answer 1 · 2015-04-16T09:57:45

Left Hand Side :

$sinx + cosx cotx$

We know that $color(blue)(cot x = cos x / sin x$

Therefore $sinx + cosx cotx = sin x + cos x* (cos x/ sinx)$

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

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

(We know the Trigonometric Identity
$color(blue)( sin^2x + cos ^ 2 x = 1$ )

$= 1 / sinx$

$= csc x$ (Because Cosecant is the reciprocal of Sine)

Hence Proved.

How do you verify sinx + cosx cotx = cscxsinx + cosx cotx = cscx?