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व्यंजक $\left[\operatorname{cosec}\left(75^{\circ}+\theta\right)-\sec \left(15^{\circ}-\theta\right)-\tan \left(55^{\circ}+\theta\right)+\cot \left(35^{\circ}-\theta\right)\right]$ का मान है
$-1$
$1$
$0$
$\frac{3}{2}$
Solution
Given, expression $=\operatorname{cosec}\left(75^{\circ}+0\right)-\sec \left(15^{\circ}-0\right)-\tan \left(55^{\circ}+0\right)+\cot \left(35^{\circ}-0\right)$
$=\operatorname{cosec}\left[90^{\circ}-\left(15^{\circ}-0\right)\right]-\sec \left(15^{\circ}-0\right)-\tan \left(55^{\circ}+0\right)+\cot \left(90^{\circ}-\left(55^{\circ}+0\right)\right\}$
$=\sec \left(15^{\circ}-0\right)-\sec \left(15^{\circ}-0\right)-\tan \left(55^{\circ}+0\right)+\tan \left(55^{\circ}+0\right)$
$\left[\therefore \operatorname{cosec}\left(90^{\circ}-0\right)=\sec 0\right.$ and $\left.\cot \left(90^{\circ}-0\right)=\tan 0\right]$
$=0$
Hence, the required value of the given expression is $0 .$
