A trigonometric equation is an equation that involves trigonometric functions, such as sine, cosine, and tangent. These equations often involve angles and can be solved by using trigonometric identities and properties.
To solve a trigonometric equation, you must use trigonometric identities and properties to manipulate the equation into a form where the variable can be isolated. Then, you can use inverse trigonometric functions to solve for the variable.
Solving a trigonometric equation allows us to find the value of a variable in an equation involving trigonometric functions. This is useful in many fields, including physics, engineering, and mathematics.
The given equation, 1+cos(180+2u) let 90+u be f, is asking us to find the value of f in terms of u. This can be done by using the trigonometric identities 1+cos(x) = 2cos^2(x/2) and cos(180+x) = -cos(x).
To solve the given equation, we first use the identity 1+cos(x) = 2cos^2(x/2) to rewrite the equation as 2cos^2(90+u/2). Then, we use the identity cos(180+x) = -cos(x) to rewrite the equation as -2cos^2(u/2). Next, we use the fact that let 90+u be f to replace u in the equation, giving us -2cos^2(f/2). Finally, we use the identity cos^2(x) = (1+cos(2x))/2 to rewrite the equation as -(1+cos(f)). Therefore, we have solved the equation and found the value of f to be -1.