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