Question

Find the value of the trigonometric equation ${\text{sin35}}^\circ {\text{ cos55}}^\circ {\text{ + cos35}}^\circ {\text{ sin55}}^\circ $

Answer 1

Hint: We convert the given equation in the question in the form of known trigonometric identity to determine the answer, using the sin (A + B) formula.

Complete step-by-step answer:
Let ${\text{A = 35}}^\circ {\text{ and B = 55}}^\circ $

We need to find,
${\text{sin35}}^\circ {\text{ cos55}}^\circ {\text{ + cos35}}^\circ {\text{ sin55}}^\circ $
⟹sinA cosB + cosA sinB sin (A + B) = sinAcosB + cosAsinB
⟹sin (A+B)
⟹${\text{sin}}\left( {{\text{35}}^\circ {\text{ + 55}}^\circ } \right)$
⟹${\text{sin}}\left( {90^\circ } \right)$
⟹1

${\text{sin35}}^\circ {\text{ cos55}}^\circ {\text{ + cos35}}^\circ {\text{ sin55}}^\circ $ = 1

Note: In order to solve this type of question, the key is to identify the form of the given equation such that it fits into one of the trigonometric formulae. Substitute the given angles in the formula to determine the answer. Refer the sine function trigonometric table for its value.