How do you verify the identity $cos x + sin x tan x = sec x$ $cosx+sinxtanx=sec x$ ?

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How do you verify the identity $cos x + sin x tan x = sec x$ $cosx+sinxtanx=sec x$ ?

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Answer 1 · 2015-05-01T11:42:37

Use the fact that:
$tan x = \frac{sin x}{cos x}$ $tanx=sinx/cosx$
and
$sec x - \frac{1}{cos x}$ $secx-1/cosx$
So:
$cos x + sin x \frac{sin x}{cos x} = \frac{1}{cos x}$ $cosx+sinxsinx/cosx=1/cosx$
$\frac{{cos}^{2} x + {sin}^{2} x}{cos x} = \frac{1}{cos x}$ $(cos^2x+sin^2x)/(cosx)=1/cosx$
$\frac{1}{cos x} = \frac{1}{cos x}$ $1/(cosx)=1/cosx$

Where I used: ${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x+cos^2x=1$

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How do you verify the identity $cos x + sin x tan x = sec x$ $cosx+sinxtanx=sec x$ ?

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How do you verify the identity $cos x + sin x tan x = sec x$ $cosx+sinxtanx=sec x$ ?