You are watching: Cos(-x)=cosx
The "co" in "cosine" way "complementary". The cosine the $ heta$ is the sine of the complementary angle to $ heta$, i m sorry is $90 - heta.$ You can see this in the appropriate triangle. If $ heta$ is one acute angle, then $90- heta$ is the other acute angle. Therefore $sin(90- heta) = $ opposing side over the hypotenuse. Yet note that, in reference to $ heta$ it is the exact same as the adjacent side end the hypotenuse.
So that"s why $sin(90- heta) = cos heta.$
Similarly, we have actually $cos(90- heta) = sin heta.$
Now take it this last identity and replace $ heta$ through $90- heta$. Girlfriend get:
$$cos(90-(90- heta)) = sin(90- heta)$$
which is
$$cos( heta) = sin(90- heta).$$
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The amount formula for sine is:-
sin(