Trigonometry – Page 141

tan-2-1-find-lets-solve-for-fun-

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Question Number 19385 by NEC last updated on 10/Aug/17 ${t a n}^{2} β = - 1$ $f i n d β \dots . l e t s s o l v e f o r f u n$ Commented by NEC last updated on 10/Aug/17 $${please}\:{help}…

If-and-are-four-solutions-of-the-equation-tan-5pi-4-3-tan-3-then-1-tan-0-2-tan-tan-2-3-tan-tan-tan-8-3-4-tan-tan-tan-tan-3-

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Question Number 19367 by Tinkutara last updated on 10/Aug/17 $If α, β, γ and δ are four solutions of the$ $equation \tan (θ + \frac{5 π}{4}) = 3 \tan 3 θ, then$ $(1) Σ \tan α = 0$ $(2) Σ \tan α \tan β = - 2$ $(3) Σ \tan α \tan β \tan γ = - \frac{8}{3}$ $(4) \tan α \tan β \tan γ \tan δ = - 3$ Answered by ajfour…

1-cos-2-3pi-2-x-cos-x-2-3-sin-x-pi-

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Question Number 84868 by jagoll last updated on 17/Mar/20 $\sqrt{1 - \cos^{2} (\frac{3 π}{2} - x)} = - \cos x + 2 \sqrt{3} \sin (x - π)$ Answered by john santu last updated on 17/Mar/20 $\cos (\frac{3 π}{2} - x) = - \sin x$ $$\mathrm{sin}\:\left(\mathrm{x}−\pi\right)\:=\:−\mathrm{sin}\:\mathrm{x} \…

Prove-the-equality-sin-pi-2n-sin-2pi-2n-sin-n-1-pi-2n-n-2-n-1-

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Question Number 19292 by Tinkutara last updated on 08/Aug/17 $Prove the equality$ $\sin \frac{π}{2 n} \sin \frac{2 π}{2 n} \dots \sin \frac{(n - 1) π}{2 n} = \frac{\sqrt{n}}{2^{n - 1}} .$ Commented by prakash jain last updated on 09/Aug/17 $$\mathrm{you}\:\mathrm{can}\:\mathrm{try}\:\mathrm{with}\:\mathrm{the}\:\mathrm{following} \…

Prove-that-1-cos-6-1-sin-24-1-sin-48-1-sin-12-

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Question Number 19291 by Tinkutara last updated on 08/Aug/17 $Prove that$ $\frac{1}{\cos 6 °} + \frac{1}{\sin 24 °} + \frac{1}{\sin 48 °} = \frac{1}{\sin 12 °} .$ Answered by Tinkutara last updated on 16/Aug/17 $\frac{1}{\cos 6 °} - \frac{1}{\sin 12 °} + \frac{1}{\sin 24 °} + \frac{1}{\sin 48 °}$ $$=\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{6}°}\:−\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{12}°}\:+\:\frac{\mathrm{sin}\:\mathrm{48}°\:+\:\mathrm{sin}\:\mathrm{24}°}{\mathrm{sin}\:\mathrm{48}°\:\mathrm{sin}\:\mathrm{24}°} \…

Let-a-b-c-be-the-sides-opposite-the-angles-A-B-and-C-respectively-of-a-ABC-Find-the-value-of-k-such-that-a-a-b-kc-b-cot-A-2-cot-B-2-k-cot-C-2-

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Question Number 19243 by Tinkutara last updated on 07/Aug/17 $Let a, b, c be the sides opposite the$ $angles A, B and C respectively of a$ $Δ ABC . Find the value of k such that$ $(a) a + b = k c$ $(b) \cot \frac{A}{2} + \cot \frac{B}{2} = k \cot \frac{C}{2} .$ Commented by Tinkutara last updated…

Prove-that-r-1-r-2-r-3-4R-r-

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Question Number 19122 by Tinkutara last updated on 05/Aug/17 $Prove that r_{1} + r_{2} + r_{3} = 4 R + r$ Answered by ajfour last updated on 05/Aug/17 $2 Rsin A = a$ $$\mathrm{r}_{\mathrm{1}}…

A-person-stands-in-the-diagonal-produced-of-the-square-base-of-a-church-tower-at-a-distance-2a-from-it-and-observes-the-angle-of-elevation-of-each-of-the-two-outer-corners-of-the-top-of-the-tower-to

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Question Number 84651 by ajfour last updated on 14/Mar/20 $A p e r s o n s t a n d s i n t h e d i a g o n a l$ $p r o d u c e d o f t h e s q u a r e b a s e o f a$ $c h u r c h t o w e r, a t a d i s t a n c e 2 a$ $f r o m i t, a n d o b s e r v e s t h e a n g l e$ $o f e l e v a t i o n o f e a c h o f t h e t w o$ $o u t e r c o r n e r s o f t h e t o p o f t h e$ $t o w e r t o b e 30 °, w h i l e t h a t o f t h e$ $${nearest}\:{corner}\:{is}\:\mathrm{45}°.\:{Find}\:{the} \…

If-tan-pi-4-x-tan-3-pi-4-then-prove-that-cosec-2x-1-3-sin-2-2-3-sin-2-sin-3-2-

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Question Number 19097 by Tinkutara last updated on 04/Aug/17 $If \tan (\frac{π}{4} + x) = \tan^{3} (\frac{π}{4} + α) then$ $prove that cosec 2 x = \frac{1 + 3 \sin^{2} 2 α}{3 \sin 2 α + \sin^{3} 2 α}$ Answered by 951172235v last updated on 01/Feb/19 $$\frac{\mathrm{cos}\:\mathrm{x}+\mathrm{sin}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}\:\:=\:\:\left(\frac{\mathrm{cos}\:\alpha+\mathrm{sin}\:\alpha}{\mathrm{cos}\:\alpha−\mathrm{sin}\:\alpha}\right)^{\mathrm{3}}…

Find-the-cubic-equation-whose-roots-are-the-radius-of-three-escribed-circles-in-term-of-inradius-circumradius-and-semiperimeter-

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Question Number 19055 by Tinkutara last updated on 03/Aug/17 $Find the cubic equation whose roots$ $are the radius of three escribed circles$ $in term of inradius, circumradius and$ $semiperimeter .$ Answered by behi.8.3.4.1.7@gmail.com last updated on 05/Aug/17…

Category: Trigonometry