Double Angle Identities Calculator

The Double Angle Identities Calculator finds the exact decimal values of sin(2θ), cos(2θ), and tan(2θ) for any angle you provide.

Step 1: Enter the angle value. Use the quick-select buttons for common angles (0°, 30°, 45°, 60°, 90°…) or type any custom value.

Step 2: Choose whether your angle is in degrees or radians.

Step 3: Click Calculate. The tool instantly displays all five forms of the double angle results, the three equivalent cos(2θ) formulas with independent verification, the tan(2θ) result (marked Undefined when it does not exist), and the underlying sin θ, cos θ, and tan θ base values.

Step 4: Tap any result card to copy that value to your clipboard.

The double angle identities express trig functions of 2θ in terms of trig functions of θ.

Sine double angle: sin(2θ) = 2·sin θ·cos θ

Cosine double angle — three equivalent forms: cos(2θ) = cos²θ − sin²θ cos(2θ) = 2cos²θ − 1 cos(2θ) = 1 − 2sin²θ

All three forms are algebraically identical. The second form is useful when you only know cos θ; the third when you only know sin θ.

Tangent double angle: tan(2θ) = 2 tan θ / (1 − tan²θ)

This is undefined when tan²θ = 1, i.e., when θ = 45°, 135°, etc.

These identities are derived by setting α = β = θ in the angle addition formulas: sin(α + β) = sin α cos β + cos α sin β cos(α + β) = cos α cos β − sin α sin β

Double angle identities are a core set of trigonometric formulas that relate the trig functions of twice an angle to those of the original angle. They arise naturally from the angle addition formulas and are widely used in calculus, signal processing, and physics.

In integration, the identities cos(2θ) = 1 − 2sin²θ and cos(2θ) = 2cos²θ − 1 are used to reduce powers before integrating (the 'power-reduction' technique). In physics and engineering, the sin(2θ) = 2 sin θ cos θ form appears in projectile range equations and wave interference calculations.

Having three separate forms for cos(2θ) is not redundant — each form is convenient in a different context depending on which trig values are already known. This calculator shows all three so that you can verify consistency and pick the most useful form for your problem.