Question:
The value of the expression $\operatorname{cosec}\left(75^{\circ}+0\right)-\sec \left(15^{\circ}-0\right)-\tan \left(55^{\circ}+0\right)+\cot \left(35^{\circ}-0\right)$ is
(a) $-1$
(b) 0
(c) 1
(d) $\frac{3}{2}$
Solution:
(b) Given, expression = cosec (75° + 0) – sec (15° – 0) – tan (55° + 0) + cot (35° – 0)
=cosec [90° – (15° – 0)] – sec (15° – 0)- tan (55° + 0) + cot (90° – (55° + 0)}
= sec (15° – 0) – sec (15° – 0) – tan (55° + 0) + tan (55° + 0)
[∴ cosec (90° – 0) = sec 0 and cot (90° – 0) = tan 0]
= 0
Hence, the required value of the given expression is 0.