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.

Basic trig identities are formulas for angle sums, differences, products, and quotients; and they let you find exact values for trig expressions.

Trigonometric Identities are the identities for trigonometry functions that are true for all the values of variables. A list of trigonometric Identities is used to solve trigonometry-related problems. Find examples at BYJU’S.

For a right triangle with an angle θ : Sine Function: sin (θ) = Opposite / Hypotenuse. Cosine Function: cos (θ) = Adjacent / Hypotenuse. Tangent Function: tan (θ) = Opposite / Adjacent. When we divide Sine by Cosine we get: So we can say: That is our first Trigonometric Identity.

Feb 28, 2025 · Trigonometric identities for Sum and Difference of angle include the formulas such as sin (A+B), cos (A-B), tan (A+B), etc. Note: Identities for sin (A+B), sin (A-B), cos (A+B), and cos (A-B) are called Ptolemy’s Identities.

Trigonometric identities include reciprocal, Pythagorean, complementary and supplementary, double angle, half-angle, triple angle, sum and difference, sum and product, sine rule, cosine rule, and a lot more. Learn all trig identities with proofs.

Mar 7, 2025 · They are based on the six fundamental trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot). All the identities are derived from the six trigonometric functions and are used to simplify expressions, verify equations, and solve trigonometric problems.

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The basic relationship between the sine and the cosine is the Pythagorean trigonometric identity: where cos 2 θ means (cos( θ )) 2 and sin 2 θ means (sin( θ )) 2 . This can be viewed as a version of the Pythagorean theorem, and follows from the equation x 2 + y 2 = 1 for the unit

Mar 7, 2025 · Double Angle Identities. Double angle identities simplify expressions where angles are doubled: Sine double angle: \sin(2\theta) = 2\sin \theta \cos \theta Cosine double angle: \cos(2\theta) = \cos^2 \theta - \sin^2 \theta Example: Find \sin(2 \cdot 30^\circ) using the double angle identity:. Identify: \theta = 30^\circ. Apply the identity: \sin(2 \cdot 30^\circ) = 2 \sin …