A geometry problem by Adi Garg

Geometry Level 3

( 1 + tan ⁡ 1 ) ( 1 + tan ⁡ 2 ) ⋯ ( 1 + tan ⁡ 45 ) = ? (1 + \tan 1 ) ( 1 + \tan 2 ) \cdots ( 1 + \tan 45) = \, ?

Angles are measured in degrees.

2^23 2^4 both a and b none of these

Adi Garg by Adi Garg , 20, India

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1 solution

Pulkit Gupta
Dec 18, 2015

As a property, 1 + tan ⁡ θ \large 1 + \tan \theta ( 1 + tan ⁡ ( π 4 − θ \large 1 + \tan ( \frac{\pi}{4} - \theta ) ) = 2.

There are 22 above such pairs and the last term evaluates to 2.

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