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3 years ago

B) A number includes only three powers of 10, but it is more than 50 000.

Mathematics

1 answer:

olga2289 [7]3 years ago

6 0

do 10 to the power of 10

50 to teh power of 3

100000 to the power of 3

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Solve the equation : <img src="https://tex.z-dn.net/?f=%20%5Ccos%28x%29%20-%20%20%5Csin%28x%29%20%20%3D%20%20%5Csqrt%7B2%20%

Debora [2.8K]

Answer:

General solution is

$x = n \pi + \frac{\pi }{8}$

Step-by-step explanation:

Step(i):-

Given cos x - sin x = √2 cos (3 x)

Dividing '√2' on both sides , we get

$\frac{1}{\sqrt{2} } cos (x) - \frac{1}{\sqrt{2} } sin (x) = \frac{\sqrt{2} cos (3 x)}{\sqrt{2} }$

we will use trigonometry formulas

a) Cos ( A + B) = Cos A Cos B - sin A sin B

b) $cos \frac{\pi }{4} = \frac{1}{\sqrt{2} }$

Step(ii):-

$\frac{1}{\sqrt{2} } cos (x) - \frac{1}{\sqrt{2} } sin (x) = \frac{\sqrt{2} cos (3 x)}{\sqrt{2} }$

$cos (\frac{\pi }{4} ) cos x - sin(\frac{\pi }{4} ) sin x = cos 3x$

$cos (\frac{\pi }{4}+x ) = cos 3 x$

Step(iii):-

General solution of cos x = cos ∝ is x = 2 nπ+∝

we have $cos (\frac{\pi }{4}+x ) = cos 3 x$

The general solution of $cos (\frac{\pi }{4}+x ) = cos 3 x$ is

⇒ $3 x = 2 n \pi + (\frac{\pi }{4}+x )$

⇒ $3 x- x = 2 n \pi + \frac{\pi }{4}$

$2x = 2 n \pi + \frac{\pi }{4}$

final answer:-

General solution is

$x = n \pi + \frac{\pi }{8}$

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