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3 years ago

X^2+12=40 what number must you add to complete the square?

Mathematics

1 answer:

posledela3 years ago

4 0

Answer:

Step-by-step explanation:

1) If you really meant X^2+12=40, then this simplifies to x^2 = 28, and therefore x = ±√28, or x = ±2√7.

2) If you meant X^2+12x=40:

a) Take half of the coefficient of x: that would be (1/2)(12), or 6.

b) Square this result, obtaining: 6² = 36

c) Add this 36 to x^2 + 12x + 40, and then subtract it: We get:

x² + 12x + 36 - 36 = 40, or x² + 12x + 36 = 76

We have to add 36, as indicated above, to "complete the square."

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3 years ago

Cos (90-theta) • cosec90-theta) =tano. How?

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Answer:

______________________________________________________

TRIGONOMETRY IDENTITIES TO BE USED IN THE QUESTION :-

For any right angled triangle with one angle α ,

$\cos (90 - \alpha ) = \sin \alpha$ or $\sin(90 - \alpha ) = \cos\alpha$

$cosec \: (90 - \alpha ) = \sec\alpha$ or $\sec(90 - \alpha ) = cosec\:\alpha$

SOME GENERAL TRIGNOMETRIC FORMULAS :-

$\sin \alpha = \frac{1}{cosec \: \alpha }$ or $cosec \: \alpha = \frac{1}{\sin \alpha }$

$\cos \alpha = \frac{1}{\sec \alpha }$ or $\sec \alpha = \frac{1}{\cos \alpha }$

______________________________________________________

Now , lets come to the question.

In a right angled triangle , let one angle be α (in place of theta) .

So , lets solve L.H.S.

$\cos (90 - \alpha ) \times cosec(90 - \alpha )$

$=> sin\alpha \times \sec\alpha$

$=> \sin\alpha \times \frac{1}{\cos\alpha }$

$=> \frac{\sin\alpha }{\cos\alpha }$

$=> \tan\alpha$ = R.H.S.

∴ L.H.S. = R.H.S. (Proved)

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3 years ago