Question

Find the exact value of the expression. Write the answer as a single fraction. Do not use a calculator.


`sin (23 \pi )/(4) cos (11 \pi )/(6) + cos (23 \pi )/(4) sin (11 \pi )/(6)`
Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize any denominators.

Answer 1

Use the rule of SINE(A+B)= SINACOSB+COSASINB

:. SIN(23pi/4+11pi/6)

-add both fractions

:. SIN(138pi/24+44pi/24)

-Simplify

:.SIN(182pi/24)

And simplify again the fraction

:.SIN(91pi/12) ---------Final answer