Ex 3.3, 11 - Chapter 3 Class 11 Trigonometric Functions (Important Question)

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Ex 3.3, 11 Prove that cos (3π/4+x) – cos (3π/4−x) = –√2 sin x Solving 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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo