If cosec θ = p + q p - q p ≠ q, p ≠ 0 , then cot π 4 + θ 2 is equals to:

Step-by-step solution

  cosec  θ = p + q p - q ⇒ 1 sin  θ = p + q p - q let tan θ 2 = t    then    1 + t 2 2t = p + q p - q ∵ sin 2 θ = 2 tan θ 1 + tan 2 θ Using componendo and dividendo rule, we get ⇒ 1 + t 2 + 2t 1 + t 2 - 2t = p + q + p - q p + q - p + q ⇒ 1 + t 1 - t 2 = p q ⇒  | 1 - t 1 + t |    = q p = | c o t ( π 4 + θ ) | ∵ tan π 4 + θ = 1 + tan θ 1 - tan θ