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Given tan(6Θ) = p/q Find the value of 1/2(pcosec2Θ – q sec2Θ)

Given tan(6Θ) = p/q Find the value of 1/2(pcosec2Θ – q sec2Θ)

Grade:12th pass

1 Answers

Faiz
107 Points
7 years ago
Tan 6x = tan 3*(2x) Using tan 3x formula.....Tan 6x = (3tan 2x - tan³ 2x) / (1 - 3 tan² 2x)Since tan 2x = sin 2x / cos 2x...replacing all and simplifying:Tan 6x = (3sin 2x cos² 2x - sin³ 2x) / (cos³ 2x - 3sin² 2x cos 2x)-> p = 3sin 2x cos² 2x - sin³ 2x-> q = cos³ 2x - 3sin² 2x cos 2xPutting value of p and q: one sin 2x gets cancelled out with cosec 2x and one cos 2x gets cancelled out with sec 2x......The expression becomes: -> 1/2 *( 3cos² 2x - sin² 2x - cos² 2x + 3sin² 2x)-> 1/2 * ( 2 sin² 2x + 2 cos² 2x )-> 1/2 * 2Ans ::::: 1

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