How do you simplify $cos x + sin x tan x$ $cos x + sin x tan x$ ?

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How do you simplify $cos x + sin x tan x$ $cos x + sin x tan x$ ?

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Answer 1 · 2018-03-26T19:16:35

$sec x$ $secx$

Explanation:

$using the trigonometric identities$ $"using the "color(blue)"trigonometric identities"$

$∙ x tan x = \frac{sin x}{cos x} and sec x = \frac{1}{cos x}$ $•color(white)(x)tanx=sinx/cosx" and "secx=1/cosx$

$∙ x {sin}^{2} x + {cos}^{2} x = 1$ $•color(white)(x)sin^2x+cos^2x=1$

$\Rightarrow cos x + sin x \times \frac{sin x}{cos x}$ $rArrcosx+sinx xx sinx/cosx$

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

$= \frac{{cos}^{2} x + {sin}^{2} x}{cos x} = \frac{1}{cos x} = sec x$ $=(cos^2x+sin^2x)/cosx=1/cosx=secx$

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How do you simplify $cos x + sin x tan x$ $cos x + sin x tan x$ ?

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