Prove that $tanx+cotx/cscx=1/cosx$ ?

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Answer 1 · 2017-02-28T07:45:35

Please see below.

$tanx+cotx/cscx$

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

= $sinx/cosx+cosx/sinx xxsinx$

= $sinx/cosx+cosx$

= $(sinx+cos^2x)/cosx$

= $(sqrt(1-cos^2x)+cos^2x)/cosx$

If it is, however, $(tanx+cotx)/cscx$

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

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

= $1/(cancelsinxcosx)xxcancelsinx$

= $1/cosx$

Prove that tanx+cotx/cscx=1/cosxtanx+cotx/cscx=1/cosx?