Question
If tan x + cot x  = 7, find  tan3 x +
cot3 x = ?Solution
We know that, (a + b)3 = a3 + b3 + 3ab (a + b) Here, a = tanx and b = cotx tan x + cot x  = 7  {cubing both the side} (tanx + cotx)3 = 73 tan 3x + cot 3 x + 3 (tanx + cotx) = 343 tan 3 x + cot 3 x = 343 - 21 = 322 Alternate solution If tan x + cot x  = N, then,we can find the value by tan3 x + cot3 x =  N 3 - 3N so, here N = 7 tan3 x + cot3 x = N 3 -3N = 7 3- 3 × 7 = 343 - 21 = 322
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