Trigonometric Prove...1

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David Cohen

IMG_20220130_130423.jpg
 
suppose that

x+1/x=2cos(θ)

show that x^2+1/x^2=2cos(3θ)

Given,
x+1/x=2cos(θ)

=>(x+1/x)^2=(2cos(θ) )^2

x^2 + 1/x^2 + 2=4cos^2(θ)

x^2 + 1/x^2 =4cos^2(θ) -2

x^2 + 1/x^2 =2(2cos^2(θ) -1)

x^2 + 1/x^2 =2cos(2 θ)
 
suppose that

x+1/x=2cos(θ)

show that x^2+1/x^2=2cos(3θ)

Given,
x+1/x=2cos(θ)

=>(x+1/x)^2=(2cos(θ) )^2

x^2 + 1/x^2 + 2=4cos^2(θ)

x^2 + 1/x^2 =4cos^2(θ) -2

x^2 + 1/x^2 =2(2cos^2(θ) -1)

x^2 + 1/x^2 =2cos(2 θ)

Thank you. I hope to solve this root tip toothache today. I cannot wait until 2/17. I am literally shedding tears.
 

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