Question:
sec210° – cot280° = ?
(a) 0
(b) 1
(c) $\frac{3}{4}$
(d) $\frac{1}{2}$
Solution:
$\sec ^{2} 10^{\circ}-\cot ^{2} 80^{\circ}$
$=\left(\sec \left(90^{\circ}-80^{\circ}\right)\right)^{2}-\cot ^{2} 80^{\circ}$
$=\operatorname{cosec}^{2} 80^{\circ}-\cot ^{2} 80^{\circ} \quad\left(\because \sec \left(90^{\circ}-\theta\right)=\operatorname{cosec} \theta\right)$
$=1 \quad$ (using the identity : $\operatorname{cosec}^{2} \theta-\cot ^{2} \theta=1$ )
Hence, the correct option is (b).
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