Question

If tan1 tan2 tan3+......tan89=1 prove that

Answer 1

tan 1.tan2.tan3........tan89
=tan1.tan2.tan3......tan44.tan45.tan46....tan88.tan89
=tan1.tan2.tan3. ......tan45.......tan (90_2)tan (90_1)
=tan1.tan2.tan3. ..tan45.....cot2.cot1
=1.1.1.1.1......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 .