Q10

Asked by omved0304 | 7th Aug, 2020, 11:24: AM

Expert Answer:

To prove that cot 4x (sin 5x + sin 3x) = cot x (sin 5x - sin 3x)
cot 4 straight x space left parenthesis sin 5 straight x space plus space sin 3 straight x right parenthesis equals fraction numerator cos 4 straight x over denominator sin 4 straight x end fraction space left parenthesis sin 5 straight x space plus space sin 3 straight x right parenthesis
equals fraction numerator cos 4 straight x over denominator sin 4 straight x end fraction open square brackets 2 sin open parentheses fraction numerator 5 straight x plus 3 straight x over denominator 2 end fraction close parentheses cos open parentheses fraction numerator 5 straight x minus 3 straight x over denominator 2 end fraction close parentheses close square brackets equals fraction numerator cos 4 straight x over denominator sin 4 straight x end fraction open square brackets 2 sin 4 straight x space cos space straight x close square brackets equals 2 space cos 4 straight x space cosx
cotx space open parentheses sin 5 straight x space minus space sin 3 straight x close parentheses equals cosx over sinx open parentheses sin 5 straight x minus sin 3 straight x close parentheses
equals fraction numerator cos 4 straight x over denominator sin 4 straight x end fraction open square brackets 2 cos open parentheses fraction numerator 5 straight x plus 3 straight x over denominator 2 end fraction close parentheses sin open parentheses fraction numerator 5 straight x minus 3 straight x over denominator 2 end fraction close parentheses close square brackets equals cosx over sinx open square brackets 2 cos 4 straight x space sinx close square brackets equals 2 space cosx space cos 4 straight x
Hence comma space cot 4 straight x space left parenthesis sin 5 straight x space plus space sin 3 straight x right parenthesis equals cotx space open parentheses sin 5 straight x space minus space sin 3 straight x close parentheses

Answered by Renu Varma | 11th Aug, 2020, 12:08: PM