Question

If sin A = $\frac{8}{17}$, find the value of secA cosA + cosecA cosA.

• A. $\frac{6}{23}$
• B. $\frac{8}{15}$
• C. $\frac{15}{8}$
• D. $\frac{23}{8}$

Answer 1

The correct option is D

$\frac{23}{8}$

sin A = $\frac{8}{17}$

cosec A = $\frac{17}{8}$

cosA = $\sqrt{1-si{n}^{2}A}$

= $\sqrt{1-\frac{64}{289}}$ = $\sqrt{\frac{225}{289}}$ = $\frac{15}{17}$

secA = $\frac{17}{15}$

secA cosA + cosecA cosA = $\frac{17}{15}$ * $\frac{15}{17}$ + $\frac{17}{15}$ * $\frac{15}{17}$

= 1 + $\frac{15}{8}$ = 2$\frac{7}{8}$

= $\frac{23}{8}$