Question

1. Convert the following products into sums or differences :
(i) 2 sin 3x cos 2x
(ii) 2 cos 3x sin 2x
(iii) 2 sin 4x sin 2x
(iv) 2 cos 7x cos 3x.​

Answer 1

hope this helps you☺️☺️☺️

Answer 2

Given:

Four equation are provided to us which are

(i) 2 sin 3x cos 2x

(ii) 2 cos 3x sin 2x

(iii) 2 sin 4x sin 2x

(iv) 2 cos 7x cos 3x.​

To Find:

Convert the following products into sums or differences.

Step-by-step explanation:

• We will solve following equations by using identities.

• (1)  2 Sin 3x Cos 2x

        We know 2Sin A CosB = Sin(A+B)+Sin(A-B)

        Using this identity we get

        2 Sin 3x Cos 2x = Sin(3x+2x)+Sin(3x-2x)

                                  = Sin5x+Sinx

• (2)  2 cos 3x sin 2x

        we know 2Cos A SinB = Sin(A+B)+Sin(A-B)

        Using this identity we get

        2 Cos 3x Sin 2x = Sin(3x+2x)+Sin(3x-2x)

                                   = Sin5x+Sinx

• (3)  2 sin 4x sin 2x

       we know 2sin A SinB = Cos(A+B)+Cos(A-B)

       Using this identity we get

       2 sin 4x sin 2x = Cos(4x+2x)+Cos(4x-2x)

                                = Cos6x+Cos2x

• (4)  2 Cos 7x Cos 3x

       we know 2cos A cosB = Cos(A+B)+Cos(A-B)

        Using this identity we get

        2 cos 7x cos 3x = Cos(7x+3x)+Cos(7x-3x)

                                   = Cos10x+Cos4x

Hence,Addition  form of following identites are

(1)2Sin3xCos2x= Sin5x +Sinx

(2)2cos3xsin2x= Sin5x +Sinx

(3)2Sin4xSin2x= Cos6x +Cos2x

(3)2cos4xcos2x= Cos10x +Cos4x