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
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 You are here
Ex 3.3, 21 Important
Example 17 Important
Misc 6 Important
cos x + cos y formula
Last updated at April 8, 2024 by Teachoo
Ex 3.3, 20 Prove that 〖sin x − 〗sin3x /(sin2x − cos2x ) = 2 sin x Solving L.H.S. 〖sin x −〗sin3x /(sin2x − cos2x ) We solve sin x – sin 3x & sin2 x – cos2 x separately sin x – sin 3x = 2 cos ((x + 3x)/2) sin((x − 3x)/2) = 2 cos (4𝑥/2) sin ((−2𝑥)/2) = 2 cos 2x sin (–x) sin2 x – cos2 x = – cos 2x We know that cos 2x = cos2 x – sin2 x cos 2x = – ( sin2 x – cos2 x) Thus, −( sin2 x – cos2 x) = cos 2x − ( sin2 x – cos2 x) = – cos 2x Now, sin〖𝑥 − sin3𝑥 〗/sin2〖𝑥 − cos2𝑥 〗 = 〖𝟐 𝒄𝒐𝒔 〗〖𝟐𝒙 〖 𝒔𝒊𝒏〗〖(−𝒙)〗 〗/〖−𝒄𝒐𝒔〗𝟐𝒙 = 〖2 𝑐𝑜𝑠〗〖2𝑥 〖(− sin〗𝑥)〗/〖−𝑐𝑜𝑠〗2𝑥 = 2sin x = R.H.S. Hence L.H.S. = R.H.S. Hence proved