write the expression as the sine, cosine, or tangent of an angle. then find the exact value of the…

write the expression as the sine, cosine, or tangent of an angle. then find the exact value of the expression.\n\\( \\sin \\frac { 7 \\pi } { 12 } \\cos \\frac { \\pi } { 12 } - \\cos \\frac { 7 \\pi } { 12 } \\sin \\frac { \\pi } { 12 } \\)\n(use integers or fractions for any numbers in the expression. simplify your answer. do not evaluate.)\n\\( \\sin \\frac { 7 \\pi } { 12 } \\cos \\frac { \\pi } { 12 } - \\cos \\frac { 7 \\pi } { 12 } \\sin \\frac { \\pi } { 12 } = \\sin \\frac { \\pi } { 2 } \\)\n(simplify your answer. type an exact answer using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)\n\\( \\sin \\frac { 7 \\pi } { 12 } \\cos \\frac { \\pi } { 12 } - \\cos \\frac { 7 \\pi } { 12 } \\sin \\frac { \\pi } { 12 } = \\square \\)

write the expression as the sine, cosine, or tangent of an angle. then find the exact value of the expression.\n\\( \\sin \\frac { 7 \\pi } { 12 } \\cos \\frac { \\pi } { 12 } - \\cos \\frac { 7 \\pi } { 12 } \\sin \\frac { \\pi } { 12 } \\)\n(use integers or fractions for any numbers in the expression. simplify your answer. do not evaluate.)\n\\( \\sin \\frac { 7 \\pi } { 12 } \\cos \\frac { \\pi } { 12 } - \\cos \\frac { 7 \\pi } { 12 } \\sin \\frac { \\pi } { 12 } = \\sin \\frac { \\pi } { 2 } \\)\n(simplify your answer. type an exact answer using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)\n\\( \\sin \\frac { 7 \\pi } { 12 } \\cos \\frac { \\pi } { 12 } - \\cos \\frac { 7 \\pi } { 12 } \\sin \\frac { \\pi } { 12 } = \\square \\)

Answer

Explanation:

Step1: Apply the sine subtraction formula

The formula for (\sin(A - B)=\sin A\cos B-\cos A\sin B). Here (A = \frac{7\pi}{12}) and (B=\frac{\pi}{12}). So, (\sin\frac{7\pi}{12}\cos\frac{\pi}{12}-\cos\frac{7\pi}{12}\sin\frac{\pi}{12}=\sin(\frac{7\pi}{12}-\frac{\pi}{12}))

Step2: Simplify the angle

(\frac{7\pi}{12}-\frac{\pi}{12}=\frac{7\pi - \pi}{12}=\frac{6\pi}{12}=\frac{\pi}{2})

Step3: Evaluate the sine function

We know that (\sin\frac{\pi}{2}=1)

Answer:

1