Buktikan identitas √2 cos (π/4 - x) = sin x + cos x Tolong bantu jawab

IdenTitaS TriGonoMetRi

√2 cos (π/4 - x) = cos x + sin x

a cos x + b sin x = k cos (x - θ)
cos x + sin x = ...
k = √(1² + 1²) = √2
tan θ = b/a = 1
θ = 45°

cos x + sin x = k cos (x - θ)
cos x + sin x = √2 cos (x - 45°)

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√2 cos (π/4 - x) = cos x + sin x
√2 cos -(x - π/4) = √2 cos (x - π/4)
√2 cos (x - π/4) = √2 cos (x - π/4)
TerBukTi

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cos (-x) = cos x