Question

Find the value of tan 1 tan 2 tan 3....tan 88 tan 89

Answer 1

Hi !

here is your answer !!

Answer is " 1 "

please see my answer step by step

thanks:

given,

Tan1° . Tan2° . Tan3°..........Tan88° . Tan89°

= Tan1° . Tan2° . Tan3°.............Tan44° . 1 . Tan ( 90° - 44° )........Tan ( 90° - 3° ) . Tan ( 90° - 2° ) . Tan ( 90° -1° )

= Tan1°. Tan2° . Tan3°.........Tan44° . Cot44°
............Cot3° . Cot2° . Cot1°

= ( Tan1° Cot1° ) ( Tan2° Cot2° ) ( Tan3° Cot3° )..............( Tan44° . Cot44° )

= 1 × 1 × 1 × ..............× 1

= 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 .

THANKS

#BeBrainly .