Question

निम्नलिखित प्रत्येक समीकरणों का व्यापक हल ज्ञात कीजिए: $\cos 3x + \cos x - \cos 2x = 0$

Answer 1

cos 3x + cos x - cos 2x = 0

[cos 3x + cos x ] - cos 2x = 0

2 cos [(3x + x)/2] .cos [(3x-x)/2] - cos 2x = 0

2 cos 2x . cos x - cos 2x = 0

cos 2x [ 2 cos x - 1 ] = 0

cos 2x = 0 or cos x = 1/2 = cos π/3

2x = (2n +1 )π/2 or x = 2mπ +- π/3

x = (2n + 1 ) π/4 or x = 2mπ +- π/3 ; where n , m ∈ I

hope this answer helpful u

Answer 2

Answer:

Step-by-step explanation:

प्रश्नानुसार   cos3x + cosx - cos2x  =  0

या        $[2cos\frac{3x+x}{2} cos\frac{3x-x}{2} ]-cos2x =0$

या         2 cos2x cosx - cos2x   =  0

या         cos2x ( 2cosx - 1 )  =  0

अतः     cos2x  =  0         या  2 cosx - 1  =  0

           cos2x  =  0          या  cosx  =   1/2

           cos2x  =  0          या  cosx  =   $cos\frac{\pi }{3}$

अतः  2x  =  (2n+1)$\frac{\pi }{2}$   याx= $2n\pi±\frac{\pi }{3}$, n∈Z

या   x =$(2n+1)\frac{\pi }{4}$        या  x =$2n\pi±\frac{\pi }{3}$ ,n∈Z