Using the identity sin^(-1)(x) + cos^(-1)(x) = π/2, we can conclude that x can take any value in the range [-1, 1].

If sin^(-1)(x) = π/4, then x = sin(π/4) = √2/2.

Using the identity tan A = sin A / cos A, we can find sin A = tan A * cos A. Using the Pythagorean identity, we find sin A = 3/5.

Since tan θ = sin θ / cos θ and tan θ = 1, we have sin θ = cos θ. For θ = 45°, sin θ = 1/√2.

If tan(x) = 1, then sin(x) = cos(x). Therefore, sin(x) + cos(x) = 2sin(x) = 2(1/√2) = √2.

tan(45°) = 1, hence x = 45°.

Using the identity tan(x) = sin(x)/cos(x), we can find sin(x) = 3/5 after applying the Pythagorean theorem.

Using the identity tan(x) = sin(x)/cos(x), we can find sin(x) = 3/5 after calculating the hypotenuse using the Pythagorean theorem.

tan(θ) = 1 at θ = 45°.

Using the identity sin²(θ) + cos²(θ) = 1, we find sin(θ) = 3/5.

tan^(-1)(x) = π/4 implies that x = tan(π/4) = 1.

According to the Arrhenius equation, an increase in activation energy results in a decrease in the rate constant k.

Using the formula A(t) = A_0 e^(-ζω_nt), we find ζ = 0.2.

Maximum velocity V_max = Aω. If A is doubled, V_max also doubles.

The total energy E in SHM is given by E = (1/2)kA². If A is doubled, E becomes (1/2)k(2A)² = 4(1/2)kA², which is quadrupled.

Maximum velocity V_max = ωA. If A is halved, V_max is also halved.

The total energy in simple harmonic motion is proportional to the square of the amplitude. If amplitude is doubled, energy increases by a factor of 2^2 = 4.

The total energy of a simple harmonic oscillator is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.

The total energy in SHM is proportional to the square of the amplitude. If amplitude is halved, energy is reduced to (1/2)^2 = 1/4, which is halved.

The energy of a wave is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.

The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.

Energy is proportional to the square of the amplitude, so if amplitude is tripled, energy increases by a factor of 3^2 = 9.

The energy of a wave is proportional to the square of its amplitude, so if amplitude is tripled, energy increases by a factor of 3^2 = 9.

If the angle is 90 degrees, the sine of the angle is zero, resulting in zero contribution to the magnetic field from that current element.

Torque is maximum when the angle is 90 degrees because τ = F × r × sin(θ) and sin(90°) = 1.

Torque (τ) = F × d × sin(θ) = 15 N × 2 m × sin(90°) = 30 Nm.

When the angle between the transmission axes of two polarizers is 90 degrees, no light passes through, resulting in zero intensity.

When the angle between the transmission axes of two polarizers is 90 degrees, no light is transmitted, resulting in zero intensity.

If the angle is 90 degrees, A · B = |A||B|cos(90) = 0.

A · B = |A||B|cos(60°) = √(2^2 + 3^2) * √(4^2 + 5^2) * 1/2 = √13 * √41 * 1/2 = 20.