Sine & Cosine

Geometry Level 1

Find the value of $\large \frac{\sin 43^\circ}{\cos 47^\circ}+\sin^2 43^\circ + \cos^2 43^\circ .$

1 solution

Anuj Shikarkhane
Apr 8, 2017

$\dfrac{\sin 43˚}{\cos 47˚}+\sin^2 43˚ + \cos^2 43˚$

= $\dfrac{\cos (90-43)˚}{\cos 47˚} + 1$ $\quad$ $\quad$ [ $\sin \theta = \cos(90-\theta), \quad \sin^2 \theta + \cos^2 \theta = 1$ ]

= $\dfrac{\cos 47˚}{\cos 47˚} +1$

= $1 + 1$

= $\boxed{2}$