Question
Question: How do you solve \(\cos x+\sin x\tan x=2\)? \[\]...
How do you solve cosx+sinxtanx=2? $$$$
Solution
We convert the tangent function in the given trigonometric equation into sine and cosine using tanθ=cosθsinθ and then we use the Pythagorean trigonometric identity sin2θ+cos2θ=1. We find trigonometric equation only cosine of the form cosx=cosα where α is principal solution whose general solution is given by x=2nπ±α.$$$$
Complete step by step answer:
We know that a trigonometric equation is an equation with trigonometric functions with unknown arguments as measure of angles. When we are asked to solve a trigonometric equation we have to find all possible measures of unknown angles.
We know that the first solution of the trigonometric equation within the interval [0,2π] is called principal solution and using periodicity all possible solutions obtained with integer n are called general solutions. The general solution of the trigonometric equation cosθ=cosα with principal solution θ=α are given by
θ=2nπ±α
Here n is any integer may be negative, positive or zero. We are given the following trigonometric equation in the question
cosx+sinxtanx=2
We convert the tangent function in the above equation into sine and cosine using tanθ=cosθsinθ in the above step to have;