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3 years ago

Prove this identity using the product-to-sum identity for sin... sin^2 x=(1-cos(2x))/(2)

Mathematics

1 answer:

Simora [160]3 years ago

4 0

Answer:

sin²x = (1 - cos2x)/2 ⇒ proved down

Step-by-step explanation:

∵ sin²x = (sinx)(sinx) ⇒ add and subtract (cosx)(cosx)

(sinx)(sinx) + (cosx)(cosx) - (cosx)(cosx)

∵ (cosx)(cosx) - (sinx)(sinx) = cos(x + x) = cos2x

∴ - cos2x + cos²x = -cos2x + (1 - sin²x)

∴ 1 - cos2x - sin²x = (1 - cos2x)/2 ⇒ equality of the two sides

∴ (1 - cos2x) - 1/2(1 - cos2x) = sin²x

∴ 1/2(1 - cos2x) = sin²x

∴ sin²x = (1 - cos2x)/2

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Answer: The answer is ASA, ed2020

Step-by-step explanation:

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3 years ago

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2 years ago

EXTRA POINTS- find the value of x and the measure of each angle

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Answer:

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Step-by-step explanation:

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2 years ago

Find an equation of a line through √3,1 / 2) parallel to the line:

vagabundo [1.1K]

Answer:

(a) $x=\sqrt{3}$

(b) $y=\frac{1}{2}$

(c) Answer of part a is equation of line $x=\sqrt{3}$ which is parallel to y axis and in part by equation of line is $y=\frac{1}{2}$ which is parallel to x axis

Step-by-step explanation:

We have given points are $(\sqrt{3},\frac{1}{2})$

(a) Equation of line is given x = -9

We have to find the equation of line parallel to x= -9 and passing through $(\sqrt{3},\frac{1}{2})$

x = -9 line is parallel to y axis and so slope will be infinite

Equation of line is given by $y-y_1=m(x-x_1)$

So $y-\frac{1}{2}=\frac{1}{0}(x-\sqrt{3})$

$x=\sqrt{3}$

(b) Equation of line is given $y=-\sqrt{7}$

This line is parallel to x axis so slope will be zero

So equation of line will be $y-\frac{1}{2}=0(x-\sqrt{3})$

$y=\frac{1}{2}$

(c) Answer of part a is equation of line $x=\sqrt{3}$ which is parallel to y axis and in part by equation of line is $y=\frac{1}{2}$ which is parallel to x axis

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3 years ago

Randall is saving money to buy a bicycle. He has $37.80 in his saving account and saves 20% of his paper route earnings each wee

DanielleElmas [232]

Answer:

In 10 weeks he saved: 87.8-37.8= $50

so each week he saves 50/10= $5

Step-by-step explanation:

So every week he earns 5*100 / 20= $25

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2 years ago