Question

cos6x+cos5x+cos4x=0 find the general solution​

Answer 1

Step-by-step explanation:

The given question is:

cos6θ+cos4θ+cos2θ+1=0

Using cosC+cosD=2cos(C+D2)cos(C−D2)and 1+cos2θ=2cos2θ we get:

⇒ 2cos5θcosθ+2cos2θ=0

⇒cosθ(cos5θ+cosθ)=0

⇒cosθ=0 [OR]cos5θ+cosθ=0

Simplifying the second expression by using cosC+cosD=2cos(C+D2)cos(C−D2) we get:

⇒2cos3θcos2θ=0

⇒ The solutions are θ∈(2n+1)π6,(2n+1)π4and(2n+1)π2

You can find the intersection of these sets to obtain the most generalized solution.