Question

Cos2theta + sin2theta = 0, solve for theta

Answer 1

• The solution for the original equation is:

theta = n pi and theta = (2n + 1)^pi/2, Where n is an integer.

Explanation:

• Rewrite the equation:

cos(2theta) + (sin(2theta) = 0

• Use the double-angle formulas:

2 cos(theta) sin(theta) + 2 sin(theta) cos(theta) = 0

• Factor out the common term:

2 sin(theta) cos(theta)(1 + 1) = 0

• Simplify:

4 sin(theta) cos(theta) = 0

• Set each factor to Zero:

For sin(theta) = 0.theta = n pi, Where n is an integer.

For cos(theta) = 0.theta = (2n + 1)^pi / 2, Where n is an integer

• Draw a conclusion:

The solution for the original equation is:

theta = n pi, and theta = (2n + 1)^pi / 2, Where n is an integer.

Hope this helps!