Trigonometric Functions · Question 23

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If 10 4 + 15 4 = 6, then the value of 27 cosec6 + 8 6 16 8 is

Answer

(1) 25

Let 2 = t, so 2 = 1 - t:

10t2 + 15(1 - t)2 = 6

⇒ 25t2 - 30t + 9 = 0

⇒ (5t - 3)2 = 0 ⇒ t = 35

∴ 2 = 35, 2 = 25

cosec6 = ( 53 )3 = 12527, 6 = ( 52 )3 = 1258, 8 = ( 52 )4 = 62516

Required value = 27 12527 + 8 125816 62516

= 250625 = 25

Answer: (1)

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