Question

proov : tan9 - tan 27 - tan63 + tan81 =4

Answer 1

tan  9 = 0.15838444
tan 27 = 0.50952545
tan 63 = 1.96261051
tan 81 =6.31375151
          = -2.31375152 + 6.31375151
          = 3.999999
          = 4

Answer 2

Answer:

Step-by-step explanation:

LHS = tan 9 - tan 27 - tan 63 + tan 81

= tan 9 - tan 27 - tan (90-27) + tan (90-9)

= tan 9 - tan 27 - cot 27 + cot 9

=[tan 9 + cot 9] - [ tan 27 + cot 27]

=[sin 9/ cos 9 + cos 9/ sin 9] - [ sin 27/cos 27 + cos 27/sin 27]

= 2/sin 18 - 2/sin 54

= 2[ 1/sin 18 - 1/ sin 54]

=2 [ (sin 54 - sin 18)/ ( sin 18 sin 54) ]

= 2 [ ( 2 cos 36 sin 18)/( sin 18 sin 54)]

= 4 cos 36 / sin 54

= 4 cos(90 - 54) / sin 54

= 4 sin 54 / sin 54

= 4