which expression is equivalent to \\( \\cos ( 103 ^ { \\circ } ) \\cos ( 54 ^ { \\circ } ) - \\sin ( 103 ^ {…

which expression is equivalent to \\( \\cos ( 103 ^ { \\circ } ) \\cos ( 54 ^ { \\circ } ) - \\sin ( 103 ^ { \\circ } ) \\sin ( 54 ^ { \\circ } ) \\)?\n\\( \\sin ( 49 ^ { \\circ } ) \\)\n\\( \\cos ( 49 ^ { \\circ } ) \\)\n\\( \\sin ( 157 ^ { \\circ } ) \\)\n\\( \\cos ( 157 ^ { \\circ } ) \\)

which expression is equivalent to \\( \\cos ( 103 ^ { \\circ } ) \\cos ( 54 ^ { \\circ } ) - \\sin ( 103 ^ { \\circ } ) \\sin ( 54 ^ { \\circ } ) \\)?\n\\( \\sin ( 49 ^ { \\circ } ) \\)\n\\( \\cos ( 49 ^ { \\circ } ) \\)\n\\( \\sin ( 157 ^ { \\circ } ) \\)\n\\( \\cos ( 157 ^ { \\circ } ) \\)

Answer

Explanation:

Step1: Recall the cosine addition formula

The formula for (\cos(A + B)=\cos A\cos B-\sin A\sin B).

Step2: Identify (A) and (B)

Here (A = 103^{\circ}) and (B=54^{\circ}). So (\cos(103^{\circ})\cos(54^{\circ})-\sin(103^{\circ})\sin(54^{\circ})=\cos(103^{\circ}+ 54^{\circ})).

Step3: Calculate (A + B)

(103^{\circ}+54^{\circ}=157^{\circ}).

Answer:

(\cos(157^{\circ}))