Question

show that cos100cos40+sin100sin40=1÷2​

Answer 1

Answer:

$cos \: 100 \degree \: cos \: 40 \degree \: + sin \: 100 \degree \: sin \: 40 \degree \: = \: \frac{1}{2}$

Step-by-step explanation:

We know that,

cos(A–B) = cos A cos B + sin A sin B

So,

L. H. S.:

$cos \: 100 \degree \: cos \: 40 \degree \: + sin \: 100 \degree \: sin \: 40 \degree \: \\ = cos \: ( \: 100 - 40 \: ) \degree \\ = cos \: 60 \degree \\ = \frac{1}{2}$

∴ LHS=RHS (Proven)