MathDB
Four Numbers

Source: 1995 National High School Mathematics League, Exam One, Problem 5

March 3, 2020

Problem Statement

The order of logsin1cos1,logsin1tan1,logcos1sin1,logcos1tan1\log_{\sin1}\cos1,\log_{\sin1}\tan1,\log_{\cos1}\sin1,\log_{\cos1}\tan1 is (form small to large) (A)logsin1cos1<logcos1sin1<logsin1tan1<logcos1tan1\text{(A)}\log_{\sin1}\cos1<\log_{\cos1}\sin1<\log_{\sin1}\tan1<\log_{\cos1}\tan1 (B)logcos1sin1<logcos1tan1<logsin1cos1<logsin1tan1\text{(B)}\log_{\cos1}\sin1<\log_{\cos1}\tan1<\log_{\sin1}\cos1<\log_{\sin1}\tan1 (C)logsin1tan1<logcos1tan1<logcos1sin1<logsin1cos1\text{(C)}\log_{\sin1}\tan1<\log_{\cos1}\tan1<\log_{\cos1}\sin1<\log_{\sin1}\cos1 (D)logcos1tan1<logsin1tan1<logsin1cos1<logcos1sin1\text{(D)}\log_{\cos1}\tan1<\log_{\sin1}\tan1<\log_{\sin1}\cos1<\log_{\cos1}\sin1