If p=csc{\theta}+cot{\theta} and q=\frac{1}{csc{\theta}-cot{\theta}}, then which of the following

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Solution

Q.
If $p = c s c θ + c o t θ a n d q = \frac{1}{c s c θ - c o t θ},$ then which of the following is/are correct

$(i) p - q = 1 (i i) p + q = 1 (i i i) p - q = 0 (i v) p + q = 0$

Choose the correct option from the following:

1 (i) and (ii)

2 (ii) and (iii)

3 (iii) and (iv)

4 (iii) only

Ans.
(4)

We know,

${c s c}^{2} θ - {c o t}^{2} θ = 1 \Rightarrow (c s c θ - c o t θ) (c s c θ + c o t θ) = 1 \Rightarrow c s c θ + c o t θ = \frac{1}{c s c θ - c o t θ} \Rightarrow p = q \Rightarrow p - q = 0$

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