cos4x cos 3x + cos2.x21.sin 4x + sin 3x +sin 2x=cot 3x,r + sin 2x
We have to prove that cos 4 x + cos 3 x + cos 2 x sin 4 x + sin 3 x + sin 2 x = cot 3 x .
The Left Hand Side of the equation.
L .H .S . = cos 4 x + cos 3 x + cos 2 x sin 4 x + sin 3 x + sin 2 x = { cos 4 x + cos 2 x } + cos 3 x { sin 4 x + sin 2 x } + sin 3 x
Use the formula.
sin A + sin B = 2 sin { A + B 2 } cos { A − B 2 } cos A + cos B = 2 cos { A + B 2 } cos { A − B 2 }
Simplify the Left Hand Side of the equation.
L .H .S . = 2 cos { 4 x + 2 x 2 } cos { 4 x − 2 x 2 } + cos 3 x 2 sin { 4 x + 2 x 2 } cos { 4 x − 2 x 2 } + sin 3 x = { 2 cos 3 x cos x + cos 3 x } { 2 sin 3 x cos x + sin 3 x } = cos 3 x { 2 cos x + 1 } sin 3 x { 2 cos x + 1 } = cot 3 x
Left hand side is equal to right hand side.
Hence proved.
We have to prove that
The Left Hand Side of the equation.
Use the formula.
Simplify the Left Hand Side of the equation.
Left hand side is equal to right hand side.
Hence proved.
