Question

express the following products into sum or difference form: sin40sin50​

Answer 1

Answer:

1/2cos10

Step-by-step explanation:

Using the formula 2sinxsiny=cos(x-y) -cos(x+y)

1/2[2sin40sin50]

1/2[cos(40-50)-cos(40+50)]

1/2[cos(-10)-cos90]

1/2[cos10-0] [cos90=0]

1/2cos10 ans.

Answer 2

Answer:

sin 40 sin 50 = $\frac{1}{2}$ [cos10 - cos 90]

Step-by-step explanation:

Given product form = sin 40 sin 50

We need to express this in sum or difference form.

We know that sin A sin B = $\frac{1}{2}$ [cos(A - B) - cos (A + B)]

On comparing the given expression to the formula, we have

A = 40 and B = 50

Therefore A - B = 40 - 50

                          = - 10

and A + B = 40 + 50

                = 90

Therefore, sin 40 sin 50 = $\frac{1}{2}$ [cos(40 - 50) - cos (40 + 50)]

                                        = $\frac{1}{2}$ [cos(-10) - cos (90)]

                                        = $\frac{1}{2}$ [cos(10) - cos (90)] (as $cos(-\theta) = cos \theta$)

Therefore, sin 40 sin 50 = $\frac{1}{2}$ [cos10 - cos 90]