Show that the equation 1+sinxtanx=5cosx can be expressed as 6cos^2-cosx-1=0?

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Answer 1 · 2017-11-12T18:48:25

See the proof below

We need

$tanx=sinx/cosx$

$sin^2x-cos^2x=1$

Therefore,

$1+sinxtanx=5cosx$

$1+sinx*sinx/cosx=5cosx$

Multiply by $cosx$

$cosx+sin^2x=5cos^2x$

Replacing $sin^2x$ by $1-cos^2x$

$cosx+1-cos^2x=5cos^2x$

$5cos^2x-cos^2x-cosx-1=0$

$6cos^2x-cosx-1=0$

$QED$