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If 10 ^4 +15 ^4 =6 , then the value of 27 cosec ^6 +8 ^6 16 ^8 is:

Options

  1. A2 5
  2. B3 4
  3. C3 5
  4. D1 5

Correct answer

A. 2 5

Step-by-step solution

aligned & 10 ( ^2 )^2+15 (1- ^2 )^2=6 & Let ^2 = t 10 t ^2+15(1- t )^2=16 & 10 t ^2+15-30 t +15 t ^2=6 & 25 t ^2-30 t +9=0 & (5 t -3)^2=0 & ^2 = 3 5 and ^2 = 2 5 & 27 125 27 +8+ 125 8 16 ( 5 2 )^4 = 250 125 5 = 2 5 aligned

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