The number of values of x -2 - 3 - satisfying -cos x-cos x-2 sin x is

Case 1: when cos x ≥0, then cos x=cos x 2sin x ⇒sin x=0 ⇒ x=2nπ, n∈ℤ nbsp; Case 2: when cos x lt; 0, then nbsp; cos x=cos x 2sin x ⇒cos x sin x =0 ⇒ ...

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Standard XII

Mathematics

General Solution of Trigonometric Equation

The number of...

Question

The number of values of $x \in [- 2 π, 3 π]$ satisfying $| cos x | = cos x - 2 sin x$ is

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Solution

Case $1 :$ when $cos x \geq 0,$ then $cos x = cos x - 2 sin x$
$\Rightarrow sin x = 0 \Rightarrow x = 2 n π, n \in Z$

Case $2 :$ when $cos x < 0,$ then
$- cos x = cos x - 2 sin x$
$\Rightarrow cos x - sin x = 0 \Rightarrow tan x = 1$
$\Rightarrow x = 2 m π + \frac{5 π}{4}, m \in Z$

In $[- 2 π, 3 π],$ values of $x$ are
$- 2 π, 0, 2 π, - \frac{3 π}{4}, \frac{5 π}{4}$
Hence, there are $5$ such values of $x$ .

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The number of values of x∈[−2π,3π] satisfying |cosx|=cosx−2sinx is

Case 1: when cosx≥0, then cosx=cosx−2sinx ⇒sinx=0⇒x=2nπ, n∈Z Case 2: when cosx<0, then −cosx=cosx−2sinx ⇒cosx−sinx=0⇒tanx=1 ⇒x=2mπ+5π4, m∈Z In [−2π,3π], values of x are −2π,0,2π,−3π4,5π4 Hence, there are 5 such values of x.

The number of values of $x \in [- 2 π, 3 π]$ satisfying $| cos x | = cos x - 2 sin x$ is