Question

Tan(p+q) = cot (p-q ) =1 find sin(2p+q )

Answer 1

Answer:

Sin(2p + q) = 1

Step-by-step explanation:

Given that-

tan(p + q) = cot(p - q) = 1

So, tan(p + q) = 1

We know that-

$tan\dfrac{\pi }{4} = 1$

So, $tan(p+q) = tan\dfrac{\pi }{4}$

$p + q = \dfrac{\pi }{4}$      ----------- 1

Now, cot(p - q) = 1

We know that-

$cot\dfrac{\pi }{4} = 1$

So, $cot(p-q) = cot\dfrac{\pi }{4}$

$p - q = \dfrac{\pi }{4}$      ------------------ 2

Adding equation 1 and 2,

We get,

$2p = \dfrac{\pi }{4}+ \dfrac{\pi }{4}$

$2p = \dfrac{\pi }{2}$

$p = \dfrac{\pi }{4}$

Put the value of p in equation 1,

We get, q = 0

Now, sin(2p+q)

= $sin[2(\dfrac{\pi }{4}) + 0]$

= $sin\dfrac{\pi }{2}$

= 1

Hence, Sin(2p + q) = 1