Question #4d51c

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Answer 1 · 2016-07-21T14:47:11

$LHS=sinx(1+tanx)+cosx(1+cotx)$

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

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

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

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

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

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

$=(1+tanx)/sinx$

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

$=cscx+secx=RHS$

Proved

Answer 2 · 2016-07-21T16:29:02

$LHS=sinx(1+tanx)+cosx(1+cotx)$

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

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

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

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

$=cancelsinx+secx-cancelcosx+cancelcosx+cscx-cancelsinx$

$secx+cscx=RHS$