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Question: If \(p = \frac{2\sin\theta}{1 + \cos\theta + \sin\theta}\), and \(q = \frac{\cos\theta}{1 + \sin\the...

If p=2sin⁡θ1+cos⁡θ+sin⁡θp = \frac{2\sin\theta}{1 + \cos\theta + \sin\theta}, and q=cos⁡θ1+sin⁡θ,q = \frac{\cos\theta}{1 + \sin\theta}, then

A

pq=1pq = 1

B

qp=1\frac{q}{p} = 1

C

q−p=1q - p = 1

D

q+p=1q + p = 1

Answer

q+p=1q + p = 1

Explanation

Solution

p=2sin⁡θ1+cos⁡θ+sin⁡θ,q=cos⁡θ1+sin⁡θp = \frac{2\sin\theta}{1 + \cos\theta + \sin\theta},q = \frac{\cos\theta}{1 + \sin\theta}

⇒p+q=cos⁡θ1+sin⁡θ+2sin⁡θ1+sin⁡θ+cos⁡θ⇒p+q=1.\Rightarrow p + q = \frac{\cos\theta}{1 + \sin\theta} + \frac{2\sin\theta}{1 + \sin\theta + \cos\theta} \Rightarrow p + q = 1.