How do you simplify $\frac{cos x - sin (\frac{π}{2} - x) sin x}{cos x - cos (π - x) tan x}$ $(cosx-sin(pi/2-x)sinx)/(cosx-cos(pi-x)tanx)$ ?

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How do you simplify $\frac{cos x - sin (\frac{π}{2} - x) sin x}{cos x - cos (π - x) tan x}$ $(cosx-sin(pi/2-x)sinx)/(cosx-cos(pi-x)tanx)$ ?

1 Answer

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Answer 1 · 2016-09-15T03:04:28

Simplify trig expression

Explanation:

Property of complementary arcs -->
$sin (\frac{π}{2} - x) = cos x$ $sin (pi/2 - x) = cos x$
Property of supplementary arcs -->
$cos (π - x) = - cos x$ $cos (pi - x) = - cos x$
$tan x = \frac{sin x}{cos x}$ $tan x = sin x/(cos x)$
The expression becomes:
$E = \frac{cos x - cos x . sin x}{cos x + sin x} =$ $E = (cos x - cos x.sin x)/(cos x + sin x) =$
$= \frac{cos x (1 - sin x)}{cos x + sin x}$ $= (cos x(1 - sin x))/(cos x + sin x)$

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How do you simplify $\frac{cos x - sin (\frac{π}{2} - x) sin x}{cos x - cos (π - x) tan x}$ $(cosx-sin(pi/2-x)sinx)/(cosx-cos(pi-x)tanx)$ ?

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Explanation:

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How do you simplify $\frac{cos x - sin (\frac{π}{2} - x) sin x}{cos x - cos (π - x) tan x}$ $(cosx-sin(pi/2-x)sinx)/(cosx-cos(pi-x)tanx)$ ?