Question

what is the value of tan75 degree​

Answer 1

Answer:

tan 75°

tan ( 45° + 30°)

tan (π/4 + π/6)

(tan π/4 + tan π/6) ÷ 1 - (tan π/4 . tan π/3)

[1 + 1/√(3)] / [1 - 1/√(3)]

= [1 + √(3)/3] / [1 - √(3)/3] .............rationalized

= [ (3 + √(3))/3] / [ (3 - √(3))/3]

= [3 + √(3)] / [3 - √(3)]

= [3 + √(3)] × [3 + √(3)] / [3 - √(3)] × [3 + √(3)]

.........rationalized

= [3 + √(3)]² / 9 - 3

= (9 + 6√(3) + 3) / 6

= (12 + 6√(3)) / 6

= 6( 2 + √(3) / 6

= 2 + √(3) is Answer ✅