which of the following is a solution for the equation 1/485 tan^2x=0
a) no solution
b) 485 pi
c) pi
d) pi/2
I'm getting conflicting answers when I try to solve it.
1/485 tan^2x=0
tan^2 x = 0
tanx = 0
so x = π , 2π, 3π, .... , 385π
x = kπ, where k is any integer
so b) and c)
To solve the equation (1/485)tan^2x = 0, we can set the equation equal to zero and solve for the value of x.
(1/485)tan^2x = 0
Since any number multiplied by zero equals zero, we can conclude that the equation is satisfied if either the coefficient (1/485) is zero or the value of tan^2x is zero.
However, the value of (1/485) cannot be zero because 1 divided by any non-zero number is not zero.
Therefore, to solve the equation, we need to find the values of x that make tan^2x equal to zero. Tan^2x is equal to zero if and only if tanx is equal to zero.
The solutions for tanx = 0 are x = n(pi), where n is an integer.
Out of the given answer choices, the only answer that satisfies this condition is:
c) pi
So, the correct solution for the equation is c) pi.
To find the solution for the equation 1/485 tan^2(x) = 0, we need to isolate tan^2(x) by multiplying both sides of the equation by 485.
1/485 tan^2(x) * 485 = 0 * 485
After canceling out the terms, we obtain:
tan^2(x) = 0
Now, we need to determine the possible solutions for this equation.
The square of a real number cannot be zero unless the number itself is zero. Therefore, the equation tan^2(x) = 0 will have a solution only if tan(x) = 0.
In trigonometry, we know that the tangent function is equal to zero at certain angles. These angles occur when the sine value is equal to zero. Sine equals zero at multiples of pi, so we can find the values of x at which tan(x) = 0 by solving the equation sin(x) = 0.
Since sin(x) = 0 at x = 0, x = pi, x = 2pi, etc., we have an infinite number of solutions. These solutions are in the form x = n*pi, where n is an integer.
However, among the given choices, none of them match the infinite solutions of the equation. Therefore, the correct answer is:
a) No solution.