Question

solve the following:-sin(n+1)x sin(n+2)x +cos(n+1)x cos(n+2)x=cosx

Answer 1

here's ur answer nd srry for bad handwriting

Answer 2

$\bold{\huge{\underline{Sloution-}}}$

$\bf \: Used \: formula- \\ \boxed{ \bf \: 1. \: cos(A - B) = cosA \: cosB + sin \: A \: sinB}$

$\bf \: L.H.S = \\ \bf \: cos(n + 1)x. \: cos(n + 2)x + sin (n + 1)x.\: sin( n+ 2)x \\ \\ \implies \bf \: cos \: (n + 2)x \: . \: cos(n + 1)x + sin(n + 2)x. \: sin(n + 1)x$

${ \bf{Now \: using \: cosA \: cosB \: + sinA \: sinB}} \\ \\ where \: (n + 2)x = A \: \: \: and \: (n + 1)x = B \:$

$\implies \bf \: cos \{(n + 2)x - ( n+ 1)x \} \\ \\ \implies \bf \: cos \: x$