Question

The value of $\sin {40}^{\circ }{35}^{\prime }\cos {19}^{\circ }{25}^{\prime }+\cos {40}^{\circ }{35}^{\prime }\sin {19}^{\circ }{25}^{\prime }$ is

• A. $\frac{1}{2}$
• B. $\frac{\sqrt{3}}{2}$
• C. $0$
• D. $-1$

Answer 1

The correct option is B $\frac{\sqrt{3}}{2}$

$\sin {40}^{\circ }{35}^{\prime }\cos {19}^{\circ }{25}^{\prime }+\cos {40}^{\circ }{35}^{\prime }\sin {19}^{\circ }{25}^{\prime }=\sin ({40}^{\circ }{35}^{\prime }+{19}^{\circ }{25}^{\prime })=\sin \left({59}^{\circ }{60}^{\prime }\right)=\sin {60}^{\circ }=\frac{\sqrt{3}}{2}$