Question

find the exact value of the expression. do not use a calculator.
\\( \sin 25 ^ { \circ } - \cos 65 ^ { \circ } \\)
\\( \sin 25 ^ { \circ } - \cos 65 ^ { \circ } = \square \\)
(simplify your answer, including any radicals. use integers or fractions for any numbers in t

Explanation:

Step1: Use co - function identity

We know that \(\cos\theta=\sin(90^{\circ}-\theta)\). So, \(\cos65^{\circ}=\sin(90^{\circ} - 65^{\circ})\).

$$ \cos65^{\circ}=\sin25^{\circ} $$

Step2: Substitute into the original expression

Substitute \(\cos65^{\circ}=\sin25^{\circ}\) into \(\sin25^{\circ}-\cos65^{\circ}\).

$$ \sin25^{\circ}-\cos65^{\circ}=\sin25^{\circ}-\sin25^{\circ} $$

Answer:

\(0\)