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AP EAMCET2006MathematicsTrigonometric Ratios & Identities

If x= 15^ , y= cosec 75^ and z=4 18^ , then :

Options

  1. Ax < y < z
  2. By < z < x
  3. Cz < x < y
  4. Dx < z < y

Correct answer

A. x < y < z

Step-by-step solution

x= 15^ = (45^ -30^ )= 45^ - 30^ 1+ 45^ 30^ = 1- 1 3 1+ 1 3 = 3 -1 3 +1 = ( 3 -1)^2 3-1 = 3+1-2 3 2 =2- 3 and y= cosec 75^ = 1 (45^ +30^ ) = 1 45^ 30^ + 45^ 30^ = 1 3 2 2 + 1 2 2 = 2 2 3 +1 3 -1 3 -1 = 2 2 ( 3 -1) 3-1 = 6 - 2 and z=4 18^ =4 ( 5 -1 4 )= 5 -1 It is clear from above that (2- 3 ) < ( 6 - 2 ) < ( 5 -1) x < y < z

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