Question

Write the expression as the sine, cosine, or tangent of an angle. cos 107° cos 42° + sin 107° sin 42°

Answer 1

Let a =107° and b=42°;

So cos 107° cos 42° + sin 107° sin 42° = cosa.cos42 + sina.sinb = cos(a-b)

and cos 107° cos 42° + sin 107° sin 42° = cos(107-42) = cos(65°)

Answer 2

Answer: It will be

`\cos65\textdegree\ and\ \sin 25\textdegree`

Explanation:

Since we have given that

cos 107° cos 42° + sin 107° sin 42°

As we know the formula :

`\cos A\cos B+\sin A\sin B=cos(A-B)`

So, applying the above formula , we get

`A=107\textdegree\\B=42\textdegree`

Now, we have to write it in cosine terms,

So, we get,

`\cos(107\textdegree-42\textdegree)=\cos65\textdegree`

So, in terms of cosine , it will be

`\cos65\textdegree`

In terms of sine , it will be

`\cos 65\textdegree=\sin(90\textdegree-65\textdegree)=\sin 25\textdegree`

Hence, it will be

`\cos65\textdegree\ and\ \sin 25\textdegree`