How do you verify $sec (x) - cos (x) = sin (x) \cdot tan (x)$ $Sec(x) - cos(x) = sin(x) * tan(x)$ ?

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How do you verify $sec (x) - cos (x) = sin (x) \cdot tan (x)$ $Sec(x) - cos(x) = sin(x) * tan(x)$ ?

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Answer 1 · 2016-03-07T20:05:15

see explanation

Explanation:

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

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

left hand side = secx - cosx = $\frac{1}{cos x} - \frac{cos x}{1}$ $1/cosx - cosx/1$

rewrite as a single fraction.

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

'split into the product of 2 functions '

$\Rightarrow = sin x . \frac{sin x}{cos x} = sin x . tan x = right hand side$ $rArr = sinx . sinx/cosx = sinx.tanx = " right hand side "$

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How do you verify $sec (x) - cos (x) = sin (x) \cdot tan (x)$ $Sec(x) - cos(x) = sin(x) * tan(x)$ ?

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How do you verify Sec(x) - cos(x) = sin(x) * tan(x)sec(x)−cos(x)=sin(x)⋅tan(x)Sec(x) - cos(x) = sin(x) * tan(x)?

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Explanation:

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How do you verify $sec (x) - cos (x) = sin (x) \cdot tan (x)$ $Sec(x) - cos(x) = sin(x) * tan(x)$ ?