Maths Olympiad Prep

Library / /47 of 520

Algebra Difficulty 1.9 Junior Find the answer

Let xx be a real number such that sec⁡x−tan⁡x=2\sec x - \tan x = 2. Then sec⁡x+tan⁡x=\sec x + \tan x =

Pick one

Solution

(sec⁡x−tan⁡x)(sec⁡x+tan⁡x)=sec⁡2x−tan⁡2x=1(\sec x - \tan x)(\sec x + \tan x) = \sec^{2} x - \tan^{2} x = 1, so sec⁡x+tan⁡x=(E) 0.5\sec x + \tan x = \boxed{\textbf{(E)}\ 0.5}.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.