How do you simplify $(1+csc x)/(cos x+ cot x)$ ?

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Answer 1 · 2015-11-08T22:31:45

$(1+cscx)/(cosx + cotx) = secx$

We will be using the following identities:

$cscx = 1/sinx$

$cotx = cosx/sinx$

$secx = 1/cosx$

$cosx + cotx = cosx(1+1/sinx) = cosx(1+cscx)$

Thus

$(1+cscx)/(cosx + cotx) = (1+cscx)/(cosx(1+cscx)) = 1/cosx = secx$

How do you simplify (1+csc x)/(cos x+ cot x)(1+csc x)/(cos x+ cot x)?