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Given Sinx^3+cosx^3+ tanx^3=0 ThenSinx^9+cosx^9+tanx^9=?A 3sinx B3sinx^2 C 9sinx^3 D 3sinx^6

Given Sinx^3+cosx^3+ tanx^3=0 ThenSinx^9+cosx^9+tanx^9=?A 3sinx B3sinx^2 C 9sinx^3 D 3sinx^6

Grade:10

1 Answers

Faiz
107 Points
7 years ago
The solution is very simple:Given : sin³x + cos³x + tan³x = 0For easy understanding let sin³x = a, cos³x = b and tan ³x = c...Identity: a³ + b³ + c³ - 3abc = ( a+b+c ) ( a² + b² + c² - ab - bc - ca )If in this a+b+c = 0 then a³ + b³ + c³ = 3 abcHence using this a³ + b³ + c³ = sin^9 x + cos^9 x + tan^9 x which is equal to 3 abc = 3 sin³x * cos³ x * tan³x....Tan x is sin x / cos x..So sin^9 x + cos^9 x + tan^9 x = 3 sin^6 x option D is the answer....

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