Cos x + cos y formula
Ex 3.3, 11 Important
Misc 3
Misc 4 Important
Ex 3.3, 14
Ex 3.3, 15
Misc 5
Misc 7 Important You are here
Example 16 Important
Ex 3.3, 16 Important
Ex 3.3, 17
Ex 3.3, 18 Important
Ex 3.3, 19
Ex 3.3, 20
Ex 3.3, 21 Important
Example 17 Important
Misc 6 Important
cos x + cos y formula
Last updated at April 16, 2024 by Teachoo
Misc 7 Prove that: sin 3x + sin2x – sin x = 4 sin x cos 𝑥/2 cos 3𝑥/2 Solving L.H.S sin 3x + sin 2x − sin x = sin 3x + (sin 2x – sin x) = sin 3x + 2cos ((2𝑥 + 𝑥)/2) . sin ((2𝑥−𝑥)/2) = sin 3x + 2 cos (𝟑𝒙/𝟐) sin 𝒙/𝟐 We know that sin 2x = 2 sin x cos x Divide by x by x/2 sin 2x/2 = 2 sin x/2 cos x/2 sin x = 2 sin x/2 cos x/2 Now Replace x by 3x sin 3x = 2 sin 𝟑𝐱/𝟐 cos 𝟑𝐱/𝟐 = 2 sin 3𝑥/2 cos 3𝑥/2 + ["2 cos " 3𝑥/2 " sin " 𝑥/2] = 2 cos 3𝑥/2 ["sin " 𝟑𝒙/𝟐 " + sin " 𝒙/𝟐] Using sin x + sin y = 2 sin (𝑥 + 𝑦)/2 cos (𝑥 − 𝑦)/2 Putting x = 3𝑥/2 & y = 𝑥/2 , = 2 cos 3𝑥/2 ["2 sin " ((3𝑥/2 " + " 𝑥/2))/2 " . cos " ((3𝑥/2 " − " 𝑥/2))/2] = 2 cos 3𝑥/2 ["2 sin " (((3𝑥 + 𝑥)/2))/2 " . cos " (((3𝑥 − 𝑥)/2))/2] = 2 cos 3𝑥/2 ["2 sin " ((4𝑥/2))/2 " . cos " ((2𝑥/2))/2] = 2 cos 3𝑥/2 ["2 sin " ((2𝑥/1))/2 " . cos " ((𝑥/1))/2] = 2 cos 𝟑𝒙/𝟐 ["2 sin " 𝟐𝒙/𝟐 " . cos " 𝒙/𝟐] = 2 cos 3𝑥/2 ["2 sin " 𝑥" . cos " 𝑥/2] = 4 cos 𝟑𝒙/𝟐 sin 𝒙 cos 𝒙/𝟐 = R.H.S Hence L.H.S = R.H.S Hence proved