Question

Prove that,
cot 4x[sin 5x + sin 3x]=cot x(sin 5x - sin 3x)​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

cot 4 x [ sin 5 x + sin 3 x ] = cot x ( sin 5 x - sin 3 x )  [ Proved ]

Step-by-step explanation:

Given :

cot 4 x [ sin 5 x + sin 3 x ] = cot x ( sin 5 x - sin 3 x )

L.H.S. = cot 4 x [ sin 5 x + sin 3 x ]

Using sum to product formula :

sin C + sin D = 2 sin ( ( C + D ) / 2 ) . cos ( ( ( C - D ) / 2 )

= > cot 4 x ( 2 sin ( 5 x + 3 x ) / 2 . cos ( 5 x - 3 x ) / 2

= > cot 4 x ( 2 sin 4 x . cos x )

= > cos 4 x / sin 4 x ( 2 sin 4 x . cos x )

= > cos 4 x ( 2 cos x )

= > 2 cos x . cos 4 x

Multiply and divide by sin x :

= > 2 cos x / sin x ( cos 4 x . sin x )

= > cot x ( 2 cos 4 x . sin x )

# 2 cos A. cos B = sin ( A + B ) - sin ( A - B )

= > cot x ( sin 5 x - sin 3 x )

Since L.H.S. = L.H.S

Hence proved.