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Prove 8. 2 / (√3 cos x + sin x) = sec((π / 6) - x)?

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  • Prove 8. 2 / (√3 cos x + sin x) = sec((π / 6) - x)?


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Answer #1 | 29/04 2014 18:38
I'm not sure why you have 8.2 in numerator. It should only be 2. If 8 is the problem number, then it's really not necessary here and just confuses things. 2 / (√3 cos x + sin x) = 1 / (√3/2 cos x + 1/2 sin x) = 1 / (cos(π/6) cosx + sin(π/6) sinx) = 1 / cos(π/6 − x) = sec(π/6 − x)
Answer #2 | 29/04 2014 19:06
cos(π/6 − x) = cos(π/6)cosx + sin(π/6)sinx) = [√3cos(x) + sin(x)]/2 sec(π/6 − x) = 1/cos(π/6 − x) = 2/[√3 cos(x) + sin(x)] It was probably question number 8.

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