### Question 2

SSC-CGL 2020 Mar 3 Shift 2

What is the value of $\displaystyle \sec(85 + \theta)$ - $\displaystyle \cosec(5 - \theta)$ + $\displaystyle \tan(35 + \theta)$ - $\displaystyle \cot(55 - \theta)$

### Solution in Brief

From trigonometry we know that

$\displaystyle \sec A = \cosec (90\degree - A)$

Using $\displaystyle A = 85\degree + \theta$, we can observe that the first two terms of the given expression become equal, and cancel out.

Again from trigonometry we know that

$\displaystyle \tan A = \cot (90\degree - A)$

Using $\displaystyle A = 35\degree + \theta$, we can observe that the last two terms of the given expression become equal, and cancel out.

Hence, the entire expression is $\displaystyle 0\:\underline{Ans}$

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