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How do you solve $4\cos x = 2$ ?

Last updated date: 14th Jun 2024
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Hint: In this question, we are given an algebraic expression in terms of x, where x is an unknown variable quantity. An algebraic expression is defined as an expression that contains both numerical values and alphabets. An algebraic expression represents a mathematical statement; a written statement can be converted into mathematical form by using the knowledge of algebra. We are given that 4 times the cosine of x is 2, thus we have to find the value of x from the given equation. Cosine is a trigonometric function, so to find the value of x, we must have the knowledge of trigonometric functions. We will first take all the constant terms to one side and then apply the arithmetic operations to find the value of x.

Complete step by step solution:
We are given $4\cos x = 2$
   \Rightarrow \cos x = \dfrac{2}{4} \\
   \Rightarrow \cos x = \dfrac{1}{2} \\
We know that
  \cos \dfrac{\pi }{3} = \dfrac{1}{2} \\
   \Rightarrow \cos x = \cos \dfrac{\pi }{3} \\
When $\cos x = \cos y$ , we get $x = y$
$ \Rightarrow x = \dfrac{\pi }{3}$

Hence, when $4\cos x = 2$ , we get $x = \dfrac{\pi }{3}$ .

Note: Trigonometric functions are those functions that tell us the relation between the two sides of a right-angled triangle and one of its angles other than the right angle. Sine, cosine, tangent, cosecant, secant and cotangent are the six functions of trigonometry. The cosine of an angle is defined as the ratio of the base of the right-angled triangle and its hypotenuse. For solving the questions related to trigonometry, we must know the trigonometric ratio of some of the basic angles like $0,\,\dfrac{\pi }{6},\,\dfrac{\pi }{4},\,\dfrac{\pi }{3},\,\dfrac{\pi }{2}$ . We can solve similar questions by using this approach.