Simplify (1+ (1/(cos2x)))∙(1+(1/(cos4x)))∙(1+(1/(cos8x)))=?


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 147933 by mathdanisur last updated on 24/Jul/21

$S i m p l i f y$ $(1 + \frac{1}{c o s 2 x}) \cdot (1 + \frac{1}{c o s 4 x}) \cdot (1 + \frac{1}{c o s 8 x}) = ?$
	Answered by som(math1967) last updated on 24/Jul/21

	$\frac{t a n x}{t a n x} (1 + \frac{1 + {t a n}^{2} x}{1 - {t a n}^{2} x}) (1 + \frac{1 + {t a n}^{2} 2 x}{1 - {t a n}^{2} 2 x})$ $\times (1 + \frac{1 + {t a n}^{2} 4 x}{1 - {t a n}^{2} 4 x})$ $= \frac{1}{t a n x} (\frac{2 t a n x}{1 - {t a n}^{2} x}) (\frac{2}{1 - {t a n}^{2} 2 x}) (\frac{2}{1 - {t a n}^{2} 4 x})$ $= \frac{1}{t a n x} \times \frac{2 t a n 2 x}{1 - {t a n}^{2} 2 x} \times \frac{2}{1 - {t a n}^{2} 4 x}$ $= \frac{1}{t a n x} \times \frac{2 t a n 4 x}{1 - {t a n}^{2} 4 x} = \frac{t a n 8 x}{t a n x}$ $[∵ t a n 2 x = \frac{2 t a n x}{1 - {t a n}^{2} x}]$
	Commented by mathdanisur last updated on 24/Jul/21

	$T h a n k y o u S e r$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum