Question

What are the solutions of a trigonometric equation? Describe the difference between verifying a trigonometric identity and solving a trigonometric equation.

Answer 1

in a trigonometric equation: eg,\[\sin(x)=0\] the solutions are all x for which the equation holds true {.... 0, 2pi, 4pi... }


a trigonometric identity is when the equation holds true FOR ALL x, eg:\[\sin^2x+\cos^2x = 1\]when verifying an identity, you use known identities / theorems to show that LHS and RHS are the same.

Answer 2

a trigonometric identity is true for all x . for example sin^2(x) + cos^2(x) = 1 , is true for all x in the reals.
but a trigonometric equation is not true for all x, its better to think of it as a conditional equation.
sin(x) = 1 , is true when x = 90 degrees . so here we go about 'solving' for x. in a trig identity there is no reason to solve for x, since the solution is all x values

Answer 3

it would be nice if they had different types of equal signs, an equal sign for identity and another for assignment, and another for conditional equations

Answer 4

there are subtle differences