Question

Find the value of tan75°
A)2/2- root 3
B)1/1-root 3
C)root 3+1/root 3-1
D)1​

Answer 1

Step-by-step explanation:

tan75°

tan(45° + 30°)

tan45° + tan30° / 1 - tan45° * tan30°

(1 + 1/√3) / ( 1 - 1/√3)

(√3 + 1)/√3 / (√3 - 1)/√3

= (√3 + 1)/(√3 - 1)

= (√3 + 1)² / (√3 - 1)(√3 + 1)

= (3 + 1 + 2√3)/(3 - 1)

= (4 + 2√3) / 2

= 2 + √3