Question

If $\tan \theta =\frac{20}{21}$ then $\sin \theta +\cos \theta$ is

• A. $\frac{29}{21}$
• B. $\frac{41}{29}$
• C. $\frac{8}{21}$
• D. $\frac{41}{8}$

Answer 1

The correct option is B $\frac{41}{29}$

Let, P, B, H be the perpendicular, base and hypotenuse of the Right angled triangle.
Given,

$\tan \theta =\frac{P}{B}=\frac{20}{21}$
$\Rightarrow P=20,B=21$

$\therefore H=\sqrt{P^2+B^2}=\sqrt{400+441}=29$

$\therefore \sin \theta =\frac{P}{H}=\frac{20}{29}$

$\cos \theta =\frac{B}{H}=\frac{21}{29}$

$\therefore \sin \theta +\cos \theta =\frac{20}{29}+\frac{21}{29}=\frac{41}{29}$

Option B is correct.