Sin2x + Cos2x=1, so Cos2x=1-Sin2x and Sin2x=1-Cos2x. Also Sin/Cos = Tan. Sec2x=1+Tan2x. Cot2x+1=Csc2x.
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In trigonometry, identities are mathematical expressions that are true for all values of the variables involved. Some common trigonometric identities include the Pythagorean identities, the reciprocal identities, the quotient identities, and the double angle identities. These identities are used to simplify trigonometric expressions and solve trigonometric equations.
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)
plane trigonometry spherical trigonometry
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.