Question #40bb3

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Question #40bb3

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Answer 1 · 2017-04-10T14:51:16

see below

Explanation:

Use the following Composite Argument Properties
$cos (A - B) = cos A cos B + sin A sin B$ $color(red)(cos(A-B)=cos A cos B+sinA sinB$
$sin (A + B) = sin A cos B + cos A sin B$ $color(red)(sin(A+B)=sinAcosB+cos A sin B$

Left Hand Side:

$cos (π - θ) + sin (\frac{π}{2} + θ) = cos π cos θ + sin π sin θ + sin (\frac{π}{2}) cos θ + cos (\frac{π}{2}) sin θ$ $color(green)(cos(pi-theta)+sin(pi/2+ theta)=color(blue)(cos picos theta+sin pi sin theta+sin (pi/2) cos theta+cos (pi/2)sin theta$

$= - 1 \cdot cos θ + 0 \cdot sin θ + 1 \cdot cos θ + 0 \cdot sin θ$ $color(blue)(=-1*cos theta+0*sin theta+1*cos theta+0*sin theta$

$= - cos θ + cos θ$ $color(blue)(=-cos theta+cos theta)$

$= 0$ $color(blue)(=0)$

$color(blue)( :.=$ Right Hand Side

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Question #40bb3

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