If cos2∝ + cos2ß = 2, then the value of tan5∝ + tan5ß is?

cos²∝ + cos2^ß = 2

⇒ 1 - sin²∝ + 1 - sin²ß = 2

⇒  sin²∝ + sin²ß = 0

⇒ sin²∝ = 0 & sin²ß = 0 ( because two positive terms give sum zero; when both are zero)

⇒ ∝ = ß = 0

⇒ tan∝ = tanß = 0

∴ tan⁵∝ + tan²ß = 0