Which of the following is the correct identity? - Vidyadip

MCQ

Which of the following is the correct identity?

A
$\cot \left(\frac{\pi}{2}+A\right)=\tan A$
✓
$\sec \left(\frac{7 \pi}{2}-A\right)=-\operatorname{cosec} A$
C
$\sin (n \pi+A)=(-1)^{2 n} \sin A$
D
$\sin (\pi-A)=-\sin A$

✓

Answer

Correct option: B.

$\sec \left(\frac{7 \pi}{2}-A\right)=-\operatorname{cosec} A$

(B)
$\sec \left(\frac{7 \pi}{2}-A\right)=\sec \left(2 \pi+\frac{3 \pi}{2}-A\right)$
$=\sec \left(\frac{3 \pi}{2}- A \right)=-\operatorname{cosec} A$

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