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 80 ^ { \\circ } \\cos 10 ^ { \\circ } + \\cos 80 ^ { \\circ } \\sin 10 ^ { \\circ } \\)\nwrite the expression as the sine, cosine, or tangent of an angle.\n\\( \\sin 80 ^ { \\circ } \\cos 10 ^ { \\circ } + \\cos 80 ^ { \\circ } \\sin 10 ^ { \\circ } = \\square ^ { \\circ } \\)\n(type an exact answer, using \\( \\pi \\) as needed. use integers or fractions for any numbers in the expression.)

write the expression as the sine, cosine, or tangent of an angle. then find the exact value of the expression.\n\\( \\sin 80 ^ { \\circ } \\cos 10 ^ { \\circ } + \\cos 80 ^ { \\circ } \\sin 10 ^ { \\circ } \\)\nwrite the expression as the sine, cosine, or tangent of an angle.\n\\( \\sin 80 ^ { \\circ } \\cos 10 ^ { \\circ } + \\cos 80 ^ { \\circ } \\sin 10 ^ { \\circ } = \\square ^ { \\circ } \\)\n(type an exact answer, using \\( \\pi \\) as needed. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Use the sine addition formula

The formula for (\sin(A + B)=\sin A\cos B+\cos A\sin B). Here (A = 80^{\circ}) and (B=10^{\circ}), so (\sin80^{\circ}\cos10^{\circ}+\cos80^{\circ}\sin10^{\circ}=\sin(80^{\circ}+ 10^{\circ})).

Step2: Calculate the value of the angle

(80^{\circ}+10^{\circ}=90^{\circ}).

Step3: Find the exact value

We know that (\sin90^{\circ}=1).

Answer:

(\sin(90^{\circ})), and the exact value is (1).