Question

Using trignometrical ratios of complementary angles prove that:

tan1*tan2*tan3........tan89 = 1

Answer 1

tan 1 . tan 2 . tan 3 ... tan 87 . tan 88 . tan 89 = LHS

tan 1 . tan 2 . tan 3 ... tan (90 - 3 ) . tan ( 90 - 2 ) . tan ( 90 - 1)

tan 1 . tan 2 . tan 3 ... cot 3 . cot 2 . cot 1

tan 1 . cot 1 . tan 2 . cot 2 . tan 3 . cot 3 ... tan 89 . cot 89

1 x 1 x 1 x 1 x ... x 1

As 1ⁿ = 1 = RHS

Where n = any positive integer