Ex 3.3, 11 - Chapter 3 Class 11 Trigonometric Functions

Transcript

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