cos (3π/4 + x) – cos (3π/4 – x) = –√2 sin x

Question

TextCosine of Sum and Difference of Two Angles

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Prove that cos (π/4 + x) + cos (π/4 – x) = √2 cos x

cos (π/4 – x) cos (π/4 – y) – sin (π/4 – x) sin (π/4 – y) = sin (x + y)

cos (π + x) cos (– x) / sin (π – x) cos (π/2 + x) = cot² x

sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x

If θ lies in the first quadrant and cos θ = 8/17, then find the value of cos(30° + θ) + cos(45° - θ) + cos(120° - θ).

Prove that: (cos 3θ + 2cos 5θ + cos 7θ)/(cos θ + 2cos 3θ + cos 5θ) = cos 2θ - sin 2θ tan 3θ.