Question

Find the value of Tan 1 degree 2 degree 3 degree........89 degree

Answer 1

Step-by-step explanation:

by use of allied angle formula

Answer 1

Answer 2

Answer:

$\bold\red{1}$

Step-by-step explanation:

$\tan(1) \tan(2) \tan(3) ........... \tan(89) \\ \\making \: pairs \: of \: these \: angles \\ \\ we \: get \\ \\ = ( \tan1 \tan89)( \tan2 \tan88)( \tan3 \tan87)........... \tan(45) \\ \\ here \: \: \tan(45) \: \: is \: unpaired \\ \\ now \\ \\ we \: know \: that \\ \\ \cot ( \alpha ) = \tan (90 - \alpha ) \\ \\ = > \ \cot (1) = \tan (90 - 1) = \tan(89) \\ \\ therefore \\ \\ we \: get \\ \\ = ( \tan1 \cot1)( \tan2 \cot2)( \tan3 \cot3)...... \tan45 \\ \\ but \\ \\ we \: know \: that \\ \\ \tan( \alpha) \cot( \alpha ) = 1 \\ \\ therefore \\ \\ we \: get \\ \\ =1 \times 1 \times 1 \times ........ \times \tan(45) \\ \\ = \tan(45) \\ \\ but \\ \\ tan \: 45 = 1$

Hence,

$\bold{Value = 1}$