Question

cos 100°.cos 40° +sin 100°.sin 40​

Answer 1

Answer:

How is cos100°.cos40°+ sin100°.sin40°= 1/2 ?

Compound formulas

Cos(A+B)=cos A.cos B-sin A.sin B

Cos(A-B)=cos A.cos B+sin A.sin B

Sin(A+B)=sin A.cos B+cos A.sin B

Sin(A-B)=sin A.cos B-cos A.sin B

Now in this question applying these formula (by cos(A-B) formula)

A=100° & B=40°

cos 100°.cos 40° + sin 100° .sin 40° =cos(100°-40°)

……………..”””””””””………………….=cos(60°)

and value of cos(60°)=1/2=0.5

Hence

Cos100°.cos40°+sin100°.sin40° = 1/2

First take the L.H.S

cos 100 .cos40 + sin 100.sin40

Here we use the formula,

cos (a-b) = cos a cos b + sin a sin b

Then L.H.S becomes,

cos (100–40) = cos 60 = 1/2 = R.H.S (proved)