Trigonometric Equations

General Solution of the equation \(a cos\theta\) + \(b sin \theta\) = c, where a, b, c \(\in\) R such that | c | \(\le\) \(\sqrt{a^2 + b^2}\). To solve this type of equations, we first reduce them in the form \(cos \theta\) = \(cos \alpha\),  or  \(sin \theta\) = \(sin \alpha\). The following algorithm […]

Here you will learn some trigonometric equation examples for better understanding of trigonometric equation concepts. Example 1 : Find general solution of (2sinx – cosx)(1 + cosx) = \(sin^2x\) Solution : (2sinx – cosx)(1 + cosx) – (1 – \(cos^2x\)) = 0 \(\therefore\)   (1 + cosx)(2sinx – cosx – 1 + cosx) = 0

Here, you will learn trigonometric equations solving strategies i.e by factorisation and reducing it to a quadratic equation etc. Let’s begin – Different Strategies for Trigonometric Equations Solving (a) Solving trigonometric equations by factorisation Example : If \(1\over 6\)sin x, cos x, tan x are in G.P. then the general solution for x is Solution