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# Use trigonometric identities to simplify the trigonometric expressions in each equation

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thanks for the help really appreciate it

Apr 27, 2021

#1
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We have,

$$sin(x+{\pi \over 2})-cos(x-\pi)=1$$

$$cosx-cos(x-\pi)=1$$

Now, we know the formula   $$cosx-cosy=-2sin{x+y\over 2}sin{x-y \over 2}$$

$$-2sin{x+x-\pi\over 2}sin{x-x+\pi\over 2}=1$$

$$-2sin({x-{\pi\over 2}})sin{\pi\over 2}=1$$

$$2sin({\pi\over 2}-x)sin{\pi\over 2}=1$$

$$2cosxsin{\pi\over 2}=1$$

$$cosx=1/2$$

$$x={\pi\over 3}$$

~Hope this helps :)

Apr 27, 2021
edited by amygdaleon305  Apr 27, 2021
#2
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Thanks :)

Guest Apr 27, 2021