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mafiozo [28]
2 years ago
13

Simplify using trigonometric identities 2sinθ - sin2θ cosθ

Mathematics
1 answer:
Anit [1.1K]2 years ago
8 0

Double angle identity for sine:

\sin(2x) = 2 \sin(x) \cos(x)

\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)

Factorize the left side.

2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)

Pythagorean identity:

\cos^2(x) + \sin^2(x) = 1

\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)

so that

\boxed{2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin^3(\theta)}

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When 9 2/3 is written in simplest radical form, which value remains under the radical?
Vera_Pavlovna [14]

Answer:

The value under the radical is 3

Step-by-step explanation:

9^(2/3) This means 9 squared then find find the cube root of the answer.

9^(2/3)=∛(9^2 )

= ∛81

= ∛(3×3×3×3) = ∛(3)³ ₓ ∛3

= 3∛3

The value under the radical is 3

I hope this now shows clearly the number under the radical is 3.

BRAINLIEST?

3 0
2 years ago
Remo needs to buy a countertop for a bathroom. He calculated the area as 10 square feet. The actual area is 9.5 square feet. Wha
Digiron [165]

Answer:

The answer is either 5.26 or 5 I think its 5.26

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4 0
3 years ago
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The quotient below is shown without the decimal point. Use number sense to place the decimal point correctly.
katrin2010 [14]

Answer:

35.8

Step-by-step explanation:

                \frac{340.1}{9.5}  = 358

 We know that our answer can never be greater than 358 since the dividend

is 340.1 and the divisor is 9.5;

  Also,

  Both values are to one decimal places and we can use this to solve the problem;

  9 can divide 340 in about 37 place with a remainder of 7,

    So, it is appropriate to make the solution 35.8

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2 years ago
Solve the system of equations<br> 3x + y = 3<br> x + y = 2
Pachacha [2.7K]

Answer:

(1/2, 3/2)

Step-by-step explanation:

solve the 1st variable in one of the equations and then substitute it and the result will be turned into the other equation.

4 0
3 years ago
I need help asap !!!!! 40 POINTS
stira [4]

Answer:

15

Step-by-step explanation:

x+5/36 = x/27

these are similar triangles

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