by proving l.h.s=r.h.s
Trigonometric identities are trigonometric equations that are always true.
Unlike equations (or inequalities), identities are always true. It is, therefore, not possible to solve them to obtain values of the variable(s).
sin^2 (feta) + cos^2 (feta) = 1 sin (feta) / cos (feta) = tan (feta)
You make them less complicated by using trigonometric relationships and identities, and then solve the less complicated questions.
Typically, the pre-requisite for calculus is algebra and trigonometry. These are usually universally required because you need these skills to actually do the mathematics of the calculus. There are a lot of identities in trigonometry that you will wish you could remember when you are working with calculus of trigonometric functions.
Yes. 'sin2x + cos2x = 1' is one of the most basic identities in trigonometry.
plane trigonometry spherical trigonometry
identities mean who you are
The main kinds are plane trigonometry and solid trigonometry. The latter will include trigonometry in hyper-spaces.
In Trig, identities are 'ultimate truths' of trigonometry. These are statements that are true regardless of the angle. Ex: sin A / cos A = tan A is true for all angles unless cos A = 0 (division by zero is undefined)
You start wit one side of the identity and, using logical steps, show that it is equivalent to the other side. Or, you start with both sides and show that they both equivalent to some common expression.