Question

Prove that tan 1 degree, tan 2 degree, tan 3 degree........ Tan 89 degree =1

Answer 1

LHS tan 1 degree,tan2 degree,tan3 degree,.....tan(90-3),tan(90-2),tan(90-1)

tan1degree, tan2 degree, tan3 degree......cot3 degree,cot2 degree,cot 3degree ( tan thitha×cot thitha=1)
so tan1 degree, tan2 degree, tan3 degree......tan89 degree =1

Answer 2

Hey there !!

Answer: 1 .

Step-by-step explanation:

= tan 1 . tan 2 . tan 3 ... tan 44 . tan 45 . tan 46 ... tan 87 . tan 88 . tan 89  

= tan 1 . tan 2 . tan 3 ... tan 44 . tan 45 . tan( 90 - 44 ) ... tan (90 - 3 ) . tan ( 90 - 2 ) . tan ( 90 - 1) 

= tan 1 . tan 2  . tan 3 ...tan44 . tan 45 . cot 44 ... cot 3 . cot 2 . cot 1 

= tan 1 . cot 1 . tan 2 . cot 2 . tan 3 . cot 3 ... tan 44 . cot 44 . tan 45 ... tan 89 . cot 89 

= 1 x 1 x 1 x ... 1 x ... x 1 . [ tan 45 = 1 ] .

= 1 .

Hence, it is solved .

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