Aman C.

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Trigonometry

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Question:

Prove the identity tan2(x) - sin2(x) = tan2(x) sin2(x)

Aman C.

Answer:

Use the identity tan(x) = sin(x) / cos(x) in the left hand side of the given identity. tan2(x) - sin2(x) = sin2(x) / cos2(x) - sin2(x) = [ sin2(x) - cos2(x) sin2(x) ] / cos2(x) = sin2(x) [ 1 - cos2(x) ] / cos2(x) = sin2(x) sin2(x) / cos2(x) = sin2(x) tan2(x) which is equal to the right-hand side of the given identity.

Algebra

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Question:

Problem Solve the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Aman C.

Answer:

Given the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13 Multiply the factors. -15x - 10 - x + 3 = -16x - 20 +13 Group like terms. -16x - 7 = -16x - 7 Add 16x + 7 to both sides and write the equation as follows 0 = 0 The above statement is true for all values of x and therefore all real numbers are solutions to the given equation

Physics

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Question:

What is the Wavelength of a Transverse Wave?

Aman C.

Answer:

The wavelength of a transverse wave is the distance between two peaks or the distance between two troughs. Wavelength can be defined as "the distance the wave has traveled during one complete cycle". Wavelength is given the symbol λ. This is the Greek letter lambda, pronounced lam-der. Wavelength is measured in meters because it is a distance.

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