Question

The value of the expression $\left[\text{cosec(75°+θ)-sec(15°-θ)-tan(55°+θ)+cot(35°-θ)}\right]$ is

• A. $-1$
• B. $0$
• C. $1$
• D. $32$

Answer 1

The correct option is B

$0$

In this question we use the formula $\text{cosec(90-θ)=secθ ,cot(90-θ)=tanθ}$

Here we use $\text{cosec(75°+θ)=cosec(90-(15-θ)),cot(35°-θ)=cot(90-(55+θ))}$

$$\begin{gathered} \text{cosec(75°+θ)-sec(15°-θ)-tan(55°+θ)+cot(35°-θ)} \\ =\text{cosec(90-(15-θ))-sec(15°-θ)-tan(55°+θ)+cot(90-(55°+θ))} \\ =\text{sec(15°-θ)-sec(15°-θ)-tan(55°+θ)+tan(55°+θ)} \\ =0 \end{gathered}$$

Hence option(B) is the correct answer and all other options are incorrect answers.