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Ex 3.3, 11 - Prove that cos (3pi/4 + x) - cos (3pi/4 - x) - cos x + cos y formula

 

  1. Class 11
  2. Important Question for exams Class 11
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Ex 3.3, 11 Prove that cos (3π/4+x) – cos (3π/4−x) = – √2 sin x Taking L.H.S. cos (3π/4+x) – cos (3π/4−x) = – 2 sin (((3π/4 + x) + (3π/4 − x))/2) sin (((3π/4 + x) − (3π/4 − x))/2) = – 2 sin (((3π/4 + 3π/4) + (𝑥 − 𝑥))/2) sin ((3π/4 + x − 3π/4 + x)/2) = – 2 sin (((3π/2 ))/2) sin (2x/2) = – 2 sin (3π/4) sin (𝑥) Putting π = 180° = – 2 sin ((3 × 180°)/4) sin (𝑥) = – 2 sin ("135°" ) sin (𝑥) = – 2 sin ( 180"°" – 45"°") sin x = – 2 sin 45° sin x = – 2 × 1/√2 × sin x = -√2 × √2 × 1/√2 × sin x = -√2 sin x = R.H.S. Hence proved

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