Given,
cos(x+3π)cos(x−3π)=41cos2(2x)
⇒2cos(x+3π)cos(x−3π)=21cos2(2x)
⇒cos(2x)+cos(32π)=21cos22x
⇒cos2x+(−21)=21cos22x
⇒cos22x−2cos2x+1=0
⇒(cos2x−1)2=0or cos2x=1
⇒2x=−6π,−4π,−2π,0,2π,4π,6π
So, x∈−3π,−2π,−π,0,π,2π,3π
So total 7 solutions.
The number of solutions of the equation cos(x+3π)cos(3π−x)=41cos22x, x∈[−3π,3π] is:
Held on 24 Jun 2022 · Verified 6 Jul 2026.
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