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AP EAMCET202317 May 2023Morning ShiftMathematicsTrigonometric EquationsActual

If , are acute angles such that =2 and 3 =2 , then ( + )=

Options

  1. A4
  2. B15
  3. C20
  4. D5

Correct answer

A. 4

Step-by-step solution

Given: =2 ...(i) and 3 =2 = 2 3 ...(ii) Now, ^2 + ^2 =(2 )^2+ ( 2 3 )^2 1=4 ( ^2 )+ 4 9 (1- ^2 ) 1=4 8 9 ^2 + 4 9 ^2 = 5 32 Now, ( + )= 1 ( + ) = 1 - = 1 2 3 ^2 -2 ^2 from equations (i) & (ii) = 1 2 3 - 8 3 ^2 = 1 2 3 - 8 3 5 32 ( + )=4

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