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steposvetlana [31]
3 years ago
14

Alex is thinking of a doubles fact. The sum is greater than the sum of 7 7 but less than the sum of 8 9. What fact is Alex think

ing of?
Mathematics
2 answers:
elena-14-01-66 [18.8K]3 years ago
6 0
There has to be something in between the two numbers, for example 7 x 7 or 7+7 not just 7 7. Without the equation it would be highly impossible to answer :D
Andrej [43]3 years ago
6 0
If it is 7+7=14 and 8+9=17 its either 15 or 16
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Solve for x: 2 over 5 (x − 4) = 2x.<br><br> −8<br> negative 1 over 2<br> 1<br> −1
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True or false. Tan^2 x = 1 - cos2x/ 1 + cos 2x
koban [17]

<u>ANSWER</u>

True

<u>EXPLANATION</u>

The given trigonometric equation is

\tan^{2} (x)  =  \frac{1 -  \cos(2x) }{1 +  \cos(2x) }

Recall the double angle identity:

\cos(2x)  =  \cos^{2} x -   \sin^{2}x

We apply this identity to obtain:

\tan^{2} (x)  =  \frac{1 - (\cos^{2} x -   \sin^{2}x) }{1 +  (\cos^{2} x -   \sin^{2}x) }

We maintain the LHS and simplify the RHS to see whether they are equal.

Expand the parenthesis

\tan^{2} (x)  =  \frac{1 - \cos^{2} x  +  \sin^{2}x }{1 +  \cos^{2} x -   \sin^{2}x}

\implies\tan^{2} (x)  =  \frac{1 - \cos^{2} x  +  \sin^{2}x }{1  -   \sin^{2}x  + \cos^{2} x }

Recall that:

1  -   \sin^{2}x  =  \cos^{2}x

1  -   \cos^{2}x  =  \sin^{2}x

We apply these identities to get:

\implies\tan^{2} (x)  =  \frac{\sin^{2}x +  \sin^{2}x }{\cos^{2} x + \cos^{2} x }

\implies\tan^{2} (x)  =  \frac{2\sin^{2}x }{ 2\cos^{2} x }

\implies\tan^{2} (x)  =  \frac{\sin^{2}x }{ \cos^{2} x }

\implies \tan^{2} (x)  =(  \frac{\sin x }{ \cos x })^{2}

Also

\frac{\sin x }{ \cos x } =  \tan(x)

\implies \tan^{2} (x)  =( \tan x )^{2}

\implies \tan^{2} (x)  =\tan^{2} (x)

Therefore the correct answer is True

5 0
3 years ago
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