Question

Simplify cos 100°.cos 40° + sin 100°.sin 40°.

Answer 1

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

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Dheeraj Kumar, studied at Dr. A.P.J. Abdul Kalam Technical University

Answered Dec 1, 2016

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°

I hope this helps you.