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In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.
Cosecant, Secant and Cotangent. We can also divide "the other way around" (such as Adjacent/Opposite instead of Opposite/Adjacent) to get: Cosecant Function: csc (θ) = Hypotenuse / Opposite. Secant Function: sec (θ) = Hypotenuse / Adjacent. Cotangent Function: cot (θ) = Adjacent / Opposite.
All the trigonometric identities are based on the six trigonometric ratios. They are sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side.
Basic trig identities are formulas for angle sums, differences, products, and quotients; and they let you find exact values for trig expressions.
After we revise the fundamental identities, we learn about: Proving trigonometric identities. But before we start to prove trigonometric identities, let's see where the basic identities come from. Recall the reciprocal trigonometric functions, csc θ, sec θ and cot θ from the trigonometric functions chapter: `csc theta=1/ (sin theta)`.
Simplify the expression by rewriting and using identities: \({\csc}^2 \theta−{\cot}^2 \theta\) Solution. We can start with the Pythagorean identity.
Pythagorean Identities. sin 2 θ + cos 2 θ = 1. tan 2 θ + 1 = sec 2 θ. cot 2 θ + 1 = csc 2 θ
