Trigonometry
Class 11

Double Angle Formula - Cosine

cos2θ=cos2θsin2θ=2cos2θ1=12sin2θ\cos 2\theta = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta
0123456−1−0.500.51
cos(2θ) = cos²θ - sin²θ

Cosine of double angle with three equivalent forms. Choose the form based on what's given in the problem.

Real-World Applications

Power reduction — Simplifying integrals: cos²x = (1+cos2x)/2.

AC power — RMS calculations in electrical engineering.

Optics — Interference pattern intensity calculations.

Signal processing — Carrier wave modulation.

Physics — Polarized light intensity (Malus's law).

Computer graphics — Texture mapping calculations.

Fourier analysis — Harmonic decomposition.

Mechanics — Vibration analysis in rotating systems.

Crystallography — X-ray diffraction calculations.

Music — Harmonic overtone analysis.

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