Question

Which expression is equivalent to sin(84°)cos(43°) + cos(84°)sin(43°)?

sin(41°)
cos(41°)
sin(127°)
cos(127°)

Answer 1

Given:

$\sin (84^\circ)\cos (43^\circ)+\cos (84^\circ)\sin (43^\circ)$

To find:

The expression that is equivalent to given expression.

Solution:

We know that,

$\sin (A+B)=\sin A\cos B+\cos A\sin B$

We have,

$\sin (84^\circ)\cos (43^\circ)+\cos (84^\circ)\sin (43^\circ)$

Here, $A=84^\circ$ and $B=43^\circ$. Using the above formula, we get

$\sin (84^\circ)\cos (43^\circ)+\cos (84^\circ)\sin (43^\circ)=\sin (84^\circ+43^\circ)$

$\sin (84^\circ)\cos (43^\circ)+\cos (84^\circ)\sin (43^\circ)=\sin (127^\circ)$

So, the equivalent expression is $\sin (127^\circ)$.

Therefore, the correct option is C.

Answer 2

Answer:

C. sin(127°)

Step-by-step explanation: