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The value of the expression
$\left[\operatorname{cosec}\left(75^{\circ}+\theta\right)-\sec \left(15^{\circ}-\theta\right)-\tan \left(55^{\circ}+\theta\right)+\right.\left.\cot \left(35^{\circ}-\theta\right)\right]$ is
$-1$
$1$
$0$
$\frac{3}{2}$
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 $0 .$
Similar Questions
Which of the following pair is correct for trigonometric inter-relationship ?
| $1 .$ $\cos \theta$ | $a.$ $\frac{\cos \theta}{\sin \theta}$ |
| $2.$ $\tan \theta$ | $b.$ $\frac{1}{\operatorname{coses} \theta}$ |
| $3 .$ $\cot \theta$ | $c.$ $\frac{1}{\sec \theta}$ |
| $4.$ $\sin \theta$ | $d.$ $\frac{1}{\cot \theta}$ |
| $e.$ $\sin \theta \cdot \cos \theta$ |
