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

Ex 3.3, 11 - Chapter 3 Class 11 Trigonometric Functions - Part 2
Ex 3.3, 11 - Chapter 3 Class 11 Trigonometric Functions - Part 3

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Transcript

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) Using cos x – cos y = –2 sin (𝑥 + 𝑦)/2 sin (𝑥 − 𝑦)/2 Putting x = 3𝜋/4 + x & y = 3𝜋/4 – x = –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 (sin (180 – 𝜃) = sin 𝜃) = −√2 sin x = R.H.S. Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.