How do you prove $sin x + cos x * cot x = csc x$ ?

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Answer 1 · 2016-11-30T14:04:57

We will use the following identities to attack the problem:

• $cotx = 1/tanx = 1/(sinx/cosx) = cosx/sinx$
• $cscx = 1/sinx$
• $cos^2x + sin^2x = 1$

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$sinx + cosx * cosx/sinx = 1/sinx$

$sinx + cos^2x/sinx = 1/sinx$

Put the left hand side on a common denominator.

$sin^2x/sinx + cos^2x/sinx = 1/sinx$

$(sin^2x + cos^2x)/sinx= 1/sinx$

$1/sinx = 1/sinx$

$LHS = RHS$

Identity proved!

Hopefully this helps!

How do you prove sin x + cos x * cot x = csc xsin x + cos x * cot x = csc x?