Question

State the whether given statement is true or false

$\sin {25}^{\circ }\cos {115}^{\circ }=(\sin {40}^{\circ }-1)$.

• A. True
• B. False

Answer 1

The correct option is B False

$\sin {25}^0\cos {115}^0=\frac{1}{2}\left(2\cos {115}^0\sin {25}^0\right)$

$=\frac{1}{2}\left(\sin ({115}^0+{25}^0)-\sin ({115}^0-{25}^0)\right)$

$=\frac{1}{2}\left(\sin \left(140^0\right)-\sin {90}^0\right)=\frac{1}{2}\left(\sin (180^0-{40}^0)-1\right)$

$=\frac{1}{2}\left(\sin {40}^0-1\right)$