Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20224 Jul 2022Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The value of tan 7 π 8 is

Options

  1. A2 - 1
  2. B1 - 2
  3. C1 + 2
  4. 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 .

Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

If x+ x= 1 2 and 0 < x < , then x= 2025If A and B are acute angles satisfying 3 ^2 A+2 ^2 B=4 and 3 A B = 2 B A , then A+2 B= 2025In a ABC , if ^2 ~B = A and 2 ^2 ~A =3 ^2 ~B , then the triangle is 202512 2 12 3 12 4 12 5 12 6 12 = 2025If ( 4 + )= ^3 ( 4 + ) , then ( + ) ( - )= 2025If A+B+C+D=2 , then A+ B+ C+ D= 2025(4 ^2 20 -1 ) (4 ^2 3 20 -1 ) (4 ^2 5 20 +1 ) (4 ^2 7 20 -1 ) (4 ^2 9 20 -1 )= 2025If A and B are the values such that (A+B) and (A-B) are not odd multiples of 2 and 2 (A+B)=3 (A-B) , then A A= 2025 Full Trigonometric Ratios & Identities list All AP EAMCET PYQs