AP EAMCET20224 Jul 2022Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual
The value of tan 7 π 8 is
Options
- A2 - 1
- B1 - 2
- C1 + 2
- D1 1 + 2
Correct answer
B. 1 - 2
Step-by-step solution
Let A = tan 7 π 8 ⇒ A = tan π - π 8 ⇒ A = - tan π 8 Now, tan π 4 = tan 2 × π 8 = 2 tan π 8 1 - tan 2 π 8 ⇒ 2 tan π 8 1 - tan 2 π 8 = 1 ⇒ 2 - A 1 - - A 2 = 1 ⇒ A 2 - 2 A - 1 = 0 ⇒ A = 2 ± 4 + 4 2 ⇒ A = 1 ± 2 But A < 0 , since 7 π 8 lies in 2 nd quadrant, where tangent angle is negative, therefore A = 1 - 2 .