MCQ
$\sec70^\circ\sin20^\circ+\cos20^\circ\text{cosec}70^\circ=?$
- A$0$
- B$1$
- C$-1$
- ✓$2$
✓
Answer
Correct option: D.
$2$
$\sec70^\circ\sin20^\circ+\cos20^\circ\text{cosec}70^\circ$
$=\frac{1}{\cos70^\circ}\times\sin20^\circ+\cos20^\circ\times\frac{1}{\sin70^\circ}$
$=\frac{1}{\cos(90^\circ-20^\circ)}\times\sin20^\circ+\cos20^\circ\times\frac{1}{\sin(90^\circ-20^\circ)}$
$=\frac{1}{\sin20^\circ}\times\sin20^\circ+\cos20^\circ\times\frac{1}{\cos20^\circ}$
$=1+1$
$=2$
$=\frac{1}{\cos70^\circ}\times\sin20^\circ+\cos20^\circ\times\frac{1}{\sin70^\circ}$
$=\frac{1}{\cos(90^\circ-20^\circ)}\times\sin20^\circ+\cos20^\circ\times\frac{1}{\sin(90^\circ-20^\circ)}$
$=\frac{1}{\sin20^\circ}\times\sin20^\circ+\cos20^\circ\times\frac{1}{\cos20^\circ}$
$=1+1$
$=2$
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