3 years ago

Solve for x 8/x +1/5 = 3/x

Mathematics

1 answer:

HACTEHA [7]3 years ago

8 0

Answer:

I think x=-25

Step-by-step explanation:

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5cosx -2sin(x/2) +7=0<br>Help me to find x step by step<br>pls

miskamm [114]

Answer:

x = 180

Step-by-step explanation:

First, you need to know

1. Double-angle formula:

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

2. Pythagorean identity:

$cos^{2}x + sin^{2}x = 1$

Back to your problem, replacing the variable by the above:

$5cosx-sin\frac{x}{2}+7 = 0$

$5(cos^{2}\frac{x}{2}-sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0$ By Double-angle formula

$5(1 - 2sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0$ By Pythagorean identity

Given $y = \frac{x}{2}$

$5(1-2sin^{2}y) - 2siny + 7 = 0$

$10sin^{2}y+2siny-12=0$

$5sin^{2}y+siny-6=0$

$(5siny + 6)(siny - 1)=0$ , we know -1 < sinx < 1, for every x ∈ R

$siny = 1, y =90$

$y = \frac{x}{2}$

$x = 180$

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