Trigonometry – Page 166

Prove-that-cos-2-x-cos-2-3x-cos-2-5x-to-n-terms-1-2-n-sin4nx-2sin2x-

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Question Number 13658 by Tinkutara last updated on 22/May/17 $Prove that$ $\cos^{2} x + \cos^{2} 3 x + \cos^{2} 5 x + \dots to n terms$ $= \frac{1}{2} [n + \frac{\sin 4 n x}{2 \sin 2 x}]$ Answered by ajfour last updated on…

Given-m-cos-sin-n-cos-sin-then-m-n-n-m-

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Question Number 144727 by imjagoll last updated on 28/Jun/21 $Given {\begin{cases} m = \cos θ - \sin θ \\ n = \cos θ + \sin θ \end{cases}$ $then \sqrt{\frac{m}{n}} + \sqrt{\frac{n}{m}} = ?$ Answered by liberty last updated on 28/Jun/21 $\Leftrightarrow \sqrt{\frac{m}{n}} + \sqrt{\frac{n}{m}} = \frac{m + n}{\sqrt{mn}}$ $$\begin{cases}{\mathrm{m}^{\mathrm{2}} =\mathrm{cos}\:^{\mathrm{2}}…

The-sum-of-the-series-sin-sin-n-4-n-2-sin-n-6-n-2-n-terms-is-equal-to-1-sin-n-2-n-2-cos-2n-2-n-3-tann-4-cotn-

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Question Number 13654 by Tinkutara last updated on 22/May/17 $The sum of the series$ $\sin θ + \sin (\frac{n - 4}{n - 2}) θ + \sin (\frac{n - 6}{n - 2}) θ + \dots n terms$ $is equal to$ $(1) \sin (\frac{n θ}{2 - n})$ $(2) \cos (\frac{2 n θ}{2 - n})$ $(3) \tan n θ$ $(4) \cot n θ$ Answered…

Given-that-x-tan-23-find-the-value-of-cos-16-in-terms-of-x-

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Question Number 144614 by nadovic last updated on 27/Jun/21 $\overset{}{} Given that x = \tan 23 °, find the value$ $of \cos 16 ° in terms of x \underset{}{.}$ Answered by qaz last updated on 27/Jun/21 $$\mathrm{x}=\mathrm{tan}\:\mathrm{23}°=\frac{\mathrm{tan}\:\mathrm{30}°−\mathrm{tan}\:\mathrm{7}°}{\mathrm{1}+\mathrm{tan}\:\mathrm{30}°\centerdot\mathrm{tan}\:\mathrm{7}°} \…

Hello-solve-in-0-2pi-tan2x-3-

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Question Number 79075 by mathocean1 last updated on 22/Jan/20 $Hello$ $solve in [0; 2 π] \tan 2 x ⩾ \sqrt{3}$ Answered by mr W last updated on 22/Jan/20 $\tan 2 x ⩾ \sqrt{3}$ $$\Rightarrow{k}\pi+\frac{\pi}{\mathrm{3}}\leqslant\mathrm{2}{x}<{k}\pi+\frac{\pi}{\mathrm{2}}…

if-a-is-a-rational-number-with-a-1-prove-that-cos-n-cos-1-a-is-also-a-rational-number-n-N-

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Question Number 79062 by mr W last updated on 22/Jan/20 $i f a i s a r a t i o n a l n u m b e r w i t h ∣ a ∣⩽ 1,$ $p r o v e t h a t \cos (n \cos^{- 1} (a)) i s a l s o a$ $r a t i o n a l n u m b e r . (n \in N)$ Answered by mind is power last updated…

solve-cosx-3-sinx-1-

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Question Number 78946 by mathocean1 last updated on 21/Jan/20 $solve$ $\cos x - \sqrt{3} s i n x = 1$ Commented by msup trace by abdo last updated on 21/Jan/20 $${e}\:\Leftrightarrow\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{2}}{cosx}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{sinx}\right)=\mathrm{1}\:\Rightarrow…

Hello-sirs-i-need-your-help-to-solve-tan2x-3-in-0-2pi-i-want-that-you-explain-me-if-possible-how-we-make-graphic-to-determinate-

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Question Number 78944 by mathocean1 last updated on 21/Jan/20 $Hello sirs i need your help to solve$ $\tan 2 x ⩾ \sqrt{3} in [0; 2 π] .$ $i want that you explain me if$ $possible how we make graphic to$ $determinate .$ Commented by mathocean1 last updated…

p-n-1-1-n-2-1-2-n-2-1-n-n-2-k-1-n-k-2-1-6-n-2n-1-n-1-show-that-1-2-1-1-n-1-12n-2-2n-1-n-1-lt-ln-p-n-lt-1-2-1-1-n-hence-find-lim-n-p-n-2-show-that

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Question Number 144483 by alcohol last updated on 25/Jun/21 $(p_{n}) = (1 + \frac{1}{n^{2}}) (1 + \frac{2}{n^{2}}) \dots (1 + \frac{n}{n^{2}})$ $\underset{k = 1}{\sum^{n}} k^{2} = \frac{1}{6} n (2 n + 1) (n + 1)$ $s h o w t h a t$ $$\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)−\frac{\mathrm{1}}{\mathrm{12}{n}^{\mathrm{2}} }\left(\mathrm{2}{n}+\mathrm{1}\right)\left({n}+\mathrm{1}\right)<{ln}\left({p}_{{n}} \right)<\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)…

If-tan-A-B-1-sec-A-B-2-3-then-prove-that-the-smallest-positive-value-of-B-is-19pi-24-

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Question Number 13403 by Tinkutara last updated on 19/May/17 $If \tan (A - B) = 1, \sec (A + B) = \frac{2}{\sqrt{3}},$ $then prove that the smallest positive$ $value of B is \frac{19 π}{24} .$ Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 19/May/17 $${excuse}\:{me}\:,{but}\:{i}\:{think}\:{your}\:{answer}\:\left(\frac{\mathrm{19}\pi}{\mathrm{24}}\right)\:{is}\:{not}\:{true}. \…

Category: Trigonometry