AP EAMCET202319 May 2023Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual
If P = 15^ + 15^ , Q = 22 1^ 2 + 22 1 2 ₂^ and R = 54^ + 18^ , then their ascending order is
Options
- AP , Q , R
- BP , R , Q
- CR , Q , P
- DR , P , Q
Correct answer
C. R , Q , P
Step-by-step solution
Given, P= 15^ + 15^ , Q= 22 1^ 2 + 22 1^ 2 and R= 54^ + 18^ Now P= 15^ 15^ + 15^ 15^ = ^2 15^ + ^2 15^ 15^ 15^ aligned & P= 1 15^ 15^ 2 2 = 2 2 15^ =2 cosec 30^ & P=2 2=4 aligned aligned & and Q= 22 1^ 2 + 22 1^ 2 = ^2 (22 1^ 2 )+ ^2 (22 1^ 2 ) (22 1^ 2 ) (22 1^ 2 ) & Q= 2 2 1 (22 1^ 2 ) (22 1^ 2 ) = 2 45^ & Q=2 2 2.83 & and R= 54^ + 18^ = (90-36)+ 18^ & = 36^ + 18^ aligned we know that aligned & 18^ = 5 -1 4 and 36^ = 5 +1 4 & R= 5 +1 4 + 5 -1 4 = 2 5 4 = 5 2 1.19 aligned Clearly R < Q < P option (c) is correct.