Question

The value of the expression $\text{cosec}({75}^0+\theta )-\sec ({15}^0-\theta )-\tan ({55}^0+\theta )+\cot ({35}^0-\theta )$, is

• A. $-1$
• B. $0$
• C. $1$
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

$0$

Given: $E=\text{cosec}({75}^0+\theta )-\sec ({15}^0-\theta )-\tan ({55}^0+\theta )+\cot ({35}^0-\theta )$

As, we know that,

$\text{cosec}\theta =\sec ({90}^0-\theta )$ and

$\tan \theta =\cot ({90}^0-\theta )$

Using these, we get

$E=\sec ({90}^0-{75}^0-\theta )-\sec ({15}^0-\theta )-\cot ({90}^0-{55}^0-\theta )+\cot ({35}^0-\theta )$
$\Rightarrow E=\sec ({15}^0-\theta )-\sec ({15}^0-\theta )-\cot ({35}^0-\theta )+\cot ({35}^0-\theta )=0$

Hence, option B is correct.