How do you simplify sin 15° cos 75° + cos 15° sin 75°?

2 Answers
Mar 1, 2018

1

Explanation:

sin 15° cos 75° + cos 15 ° sin 75 °
=sin(15°+75°)=sin(90)=1

Mar 1, 2018

"We have the answer:"

\qquad \qquad \qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ 1.

Explanation:

"The expression given matches the pattern of the formula for"
sin( x + y ). \ \ "Recall that formula:"

\qquad \qquad \qquad \qquad \quad \quad sin( x + y ) \ = \ sinx cosy + cos x siny.

"Now write it in the reverse direction:"

\qquad \qquad \qquad \qquad \quad \quad sinx cosy + cos x siny \ = \ sin( x + y ).

"Now, if in the reverse direction of that formula, we let:"

\qquad \qquad \qquad \qquad \qquad \qquad \qquad x = 15^@ \qquad "and" \qquad y = 75^@;

"we get:"

\qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ sin( 15^@ + 75^@ ).

"Thus:"

\qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ sin( 90^@ ) \ = \ 1.

"So we have the following simplification result:"

\qquad \qquad \qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ 1.