Find value of tan7°.tan14°.tan21°.tan28°.tan83°.tan76°.tan69°.tan62°

1 \(\sqrt {3 }\) 2\(\sqrt {2 }\) 2\(\frac{\sqrt {2} + 3}{2}\)

1

(tan7°.tan83°)(tan14°.tan76°)(tan21°.tan69°)(tan28°.tan62°) = (tan7°.cot7°)(tan14°.cot14°)(tan21°.cot21°)(tan28°.cot28°) = 1  (because tanθ = cot(90- θ)) tanθ.cotθ = 1