Prove that sin2nx+ cos2nx ≤ 1 for all x and n≥1

Dear Manoj,

0<=sin^2(x) ,cos^2(x)<=1 for all x

therefore , sin^2n(x) <=sin^2x and cos^2n(x)<=cos^2(x) for n>=1

adding both we get  sin²ⁿx +  cos²ⁿx ≤ 1

 

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