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

User Lanorkin
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2 Answers

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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°)
User Mehyar Sawas
by
8.8k points
7 votes

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

User Aviro
by
8.0k points
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