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2 years ago

Solve the equation: sin(2x)= sin x

Mathematics

1 answer:

Anna [14]2 years ago

3 0

Answer:

Below

Step-by-step explanation:

sin(2x) = 2 ×cos(x)× sin(x)

● sin(x) = 2 × cos(x) × sin(x)

● 2 × cos(x) = 1

● cos (x) = 1/2

So we can deduce that:

● x = Pi/3 + 2*k*Pi

● or x = -Pi/3 + 2*k*Pi

K is an integer

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3 years ago

What two numbers multiply to 10 and add to -29 ?

Degger [83]

Xy=10
x+y=29

subtract x from both sides for second equation

y=-x-29
subsitute in second equaiton
x(-x-29)=10
-x^2-29x=10
add x^2+29x to both sides
x^2+29x+10=0
quadratic formula
if you have
ax^2+bx+c=0,
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

so
x^2+29x+10=0
a=1
b=29
c=10
x= $\frac{-29+/- \sqrt{(-29)^{2}-4(1)(10)} }{2(1)}$
x= $\frac{-29+/- \sqrt{841-40} }{2}$
x= $\frac{-29+/- \sqrt{801} }{2}$
x= $\frac{-29+/- 3\sqrt{89} }{2}$

x= $\frac{-29- 3\sqrt{89} }{2}$ or $\frac{-29+ 3\sqrt{89} }{2}$
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2 years ago

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