3 years ago

The ordered pairs (1,6), (,25), (3,36), (4,49) and (5, 64) represent a function. what is a rule that represents this function?

1 answer:

7 0

I believe this is a function. I am not sure because one of the pairs only has a y value.
But the rule is there can only be one x value for one y value so for example, you can have (3.7) and (3,9) and the same for the y values.

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2 years ago

(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x

Aliun [14]

As

$\tan x=\dfrac{\sin x}{\cos x}$
$\cot x=\dfrac{\cos x}{\sin x}$

we have

$\sin x(\tan x\cos x-\cot x\cos x)=\sin x\left(\sin x-\dfrac{\cos^2x}{\sin x}\right)=\sin^2x-\cos^2x$

Recalling that $\cos2x=\cos^2x-\sin^2x$ , we end up with

$-\cos2x=1-2\cos2x$
$1=\cos2x$
$\implies2x=2n\pi$

(where $n$ is any integer)

$\implies x=n\pi$