How do you prove $tanx + cotx = secx cscx$ ?

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Answer 1 · 2015-11-28T03:04:30

Please follow the step below

Given:
$tan x+ cot x= sec x *cscx$

Start on the right hand side, change it to $sinx$ ; $cosx$

$sinx/cosx + cosx/sinx = sec x *csc x$

$color(red)([sinx/sinx])*(sinx/cosx)$ + $color(blue) [cosx/cosx]*cosx/sinx$ = $sec x*cscx$

$[sin^2x+cos^2x]/(sinx*cosx) = sec x *cscx$

$1/(sinx *cos x) = sec x *csc x$

$(1/sinx)(1/cosx) = secx*cscx$

$sec x *csc x = secx *csc x$

Prove completed!

* $sin^2x + cos^2x= 1$

* $1/sinx = csc x$ ; $1/cosx = secx$

How do you prove tanx + cotx = secx cscxtanx + cotx = secx cscx?