How do you prove: $cos x + sin x tan x = sec x$ $Cosx + sinx tanx = secx$ ?

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Answer 1 · 2018-03-04T05:03:03

See below.

We have:

$L H S = cos x + sin x tan x$ $LHS=cosx+sinxtanx$ and $R H S = sec x$ $RHS=secx$

We change the $L H S$ $LHS$ :

$cos x + sin x \cdot \frac{sin x}{cos x}$ $cosx+sinx*sinx/cosx$

$= cos x + \frac{{sin}^{2} x}{cos x}$ $= cosx+sin^2x/cosx$

$= \frac{{sin}^{2} x + {cos}^{2} x}{cos x}$ $= (sin^2x+cos^2x)/cosx$

$= \frac{1}{cos x}$ $= 1/cosx$

$= sec x$ $= secx$

So $L H S = R H S$ $LHS=RHS$

Hence, proved.

How do you prove: cosx+sinxtanx=secxCosx + sinx tanx = secx?