NEB Class 11 Mathematics: General Solutions of Trigonometric Equations

General solutions require integer parameter $n \in \mathbb{Z}$ formulas:

• $\sin\theta = \sin\alpha \implies \theta = n\pi + (-1)^n \alpha$
• $\cos\theta = \cos\alpha \implies \theta = 2n\pi \pm \alpha$
• $\tan\theta = \tan\alpha \implies \theta = n\pi + \alpha$

For $a\cos\theta + b\sin\theta = c$, divide through by $r = \sqrt{a^2 + b^2}$ to condense the expression into a single cosine identity.