The number of values of x in -0-2 - satisfying the equation 3 cos 2 x-10 cos x-7-0 isA- 1B- 2C- 3D- 4

The correct option is D 4 Given, 3 cos2x 10 cosx + 7 = 0 ⇒ 3 ( 2cos^2x 1 ) 10cosx+7=0 ⇒ 3cos^2 x 5cosx+2=0 ⇒ ( 3cosx 2 ) ( cosx 1 )=0 ⇒ cosx=1 or cosx=2/ ...

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Standard XII

Mathematics

General Solution of Trigonometric Equation

The number of...

Question

The number of values of x in $[0, 2 π]$ satisfying the equation 3 cos2x - 10 cosx + 7 = 0 is

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Solution

The correct option is D
4

Given,

3 cos2x - 10 cosx + 7 = 0

$\Rightarrow 3 (2 c o s^{2} x - 1) - 10 c o s x + 7 = 0$

$\Rightarrow 3 c o s^{2} x - 5 c o s x + 2 = 0$

$\Rightarrow (3 c o s x - 2) (c o s x - 1) = 0$

$\Rightarrow c o s x = 1 o r c o s x = \frac{2}{3}$

Here, four values exist , when $x \in [0, 2 π]$

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The number of values of x in [0, 2π]satisfying the equation 3 cos2x - 10 cosx + 7 = 0 is

The correct option is D 4 Given, 3 cos2x - 10 cosx + 7 = 0 ⇒3(2cos2x−1)−10cosx+7=0 ⇒3cos2x−5cosx+2=0 ⇒(3cosx−2)(cosx−1)=0 ⇒cosx=1 or cosx=23 Here, four values exist , when x∈[0,2π]

The number of values of x in $[0, 2 π]$ satisfying the equation 3 cos2x - 10 cosx + 7 = 0 is