Trigonometric Formulas

Knowing basic trigonometric identities is essential for simplifying complex expressions.

Fundamental Identities:

• $\sin^2\theta + \cos^2\theta = 1$
• $1 + \cot^2\theta = \csc^2\theta$
• $\tan^2\theta + 1 = \sec^2\theta$

Sum/Difference & Double Angle Formulas:

• $\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$
• $\cos(a \pm b) = \cos a \cos b \mp \sin a \sin b$
• $\sin(2a) = 2\sin a \cos a$
• $\cos(2a) = \cos^2a - \sin^2a$

For example, $\sin(10°)\cos(20°) + \cos(10°)\sin(20°)$ simplifies to $\sin(10°+20°) = \sin(30°) = 1/2$.