Unanswered Trignometry Questions

i find it hard to these questions........... so plz help 1) (2cos40 -cos20)/sin20 2) tan10-tan50+tan70 ...

Prove that in every triangle we have: ma*mb>=ra*rb*rc. ma is length of median drawn from A, same is mb. ra= exradius of A ...

[sry i deleted it] ...

If a right angle is divided into three parts α,β,γ prove that for all possible divisons, tanα+tanβ+tanγ>1+tanαtanβtanγ ...

If cosx+cosy+cosz=0 & cos3x+cos3y+cos3z=0 the prove that cos2x.cos2y.cos2z≤0 x,y,zε R All the sirs plz dont post the soln to this one[1] ...

please prove these identities : $ \sin (\frac{\pi}{2m})\sin (\frac{2\pi}{2m})\sin (\frac{3\pi}{2m})\dots\sin (\frac{(m-1)\pi}{2m}) =\frac{\sqrt{m}}{2^{m-1}} $ \sin (\frac{\pi}{4m})\sin (\frac{3\pi}{4m})\sin (\frac{5\pi}{4m})\ ...

If cos4θ.sec2α, 1/2 and sin4θ.cosec2α are in AP, then cosec8θsec6α , 1/2, sin8θ.cosec6α are in a)AP b)GP c)HP d)none ans a) ...

find the angles and the side lengths of the pedal triangle of triangle ABC ....a ,b ,c as usual side lengths of triangle ABC with angle A B and C **EDITED** LEAVE IT I GOT IT ...

\sum_{r=0}^{9}{\left(-1 \right)^r\cos^{10}\frac{r\pi}{10}} any short solution using complex? ...

cosnθ = [P][/n] (cosθ) [P][/n] is a polynomial of degree n like [P][/2] = 2x^{2}-1 (n is a natural no.) then find (x+\sqrt{x^{2}-1})^{n} +(x-\sqrt{x^{2}-1})^{n} in terms of [P][/n] ...

In a triangle ABC ,AD is the perpendicular to BC .the inradii of ADC,ADB and ABC are x,y,z .find the relation between x ,y and z? note::the relationship shud have only x y and z.....no oder variable. ...

for practice \text{if x,y,and z are the distances from vetrices A,B,and C to orthocentre respectively then prove that }\\ \frac{a}{x}+\frac{b}{y}+\frac{c}{z}=\frac{abc}{xyz} ...

is tata mvgraw hill course in maths good? ...

Find general value of x which satsfies the equation 2sin(3x+ π/4 ) = 1+8sin2x cos22x . ...

If θ is the fundamental period of the function f(x) = sin99x + sin99(x + 2π/3) + sin99(x + 4π/3), then the complex number z = r(cosθ + isinθ) lies in the quadrant??? I m getting θ= 2π/3 and hence the ans should be 2... ...

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$\textbf{If $\mathbf{S=(sin\;x+sin\;2x+sin\;4x)^5 -(-sin\;x+sin\;2x+sin\;4x)^5-(sin\;x-sin\;2x+sin\;4x)^5-(sin\;x+sin\;2x-sin\;4x)^5$}}$\\\\ $\textbf{Then Calculate value of $\mathbf{S}$ at $\mathbf{x=20^0}$}. ...

hi frnds, I am confused. i am getting two different answers .help me out. Solve; 4sin(2x) + 3 cos (2x) =5 My solution is: 4(2sinx cos x) + 3 (2cos2x - 1) =5 →8sinx cosx + 6cos2x = 8 Divide both sides by cos2x →8tanx + 6 = ...

\hspace{-16}$Show that the equation\\\\ $\mathbf{e^{1-\tan^{-1}x}+\tan^{-1}(e^x-1)=2}$\\\\ has no solution for $x\in\mathbb{R}$ ...

\hspace{-16}$It is known about real $\mathbf{a}$ and $\mathbf{b}$ that the inequality $\mathbf{a\; cosx +b\;cos3x >1}$\\\\ has no real solutions.then Prove that $\mathbf{\mid b\mid \leq 1}. ...

\text{The equation} (1+k)\cdot\frac{\cos x\cdot\cos(2x-\alpha)}{\cos(x-\alpha )} =1+k\cos 2x \; has no repeated root in it's domain of definition, if : a) |k| ≤ |csc α| , k ≠± 1 a) |k| ≤ |csc α| , k ≠- 1 a) |k| ≥ ...

\hspace{-16}$Calculate Sum of \\\\ $\mathbf{(1)\;\; \cos^{2n}1^{\arc0}+\cos^{2n}2^{\arc0}+\cos^{2n}3^{\arc0}+\cos^{2n}4^{\arc0}+..........+\cos^{2n}89^{\arc0}=}$\\\\ $\mathbf{(2)}$ \;\; Prove that $\mathbf{\cos^{10}1^{\arc0}+ ...

For x>0, and A,B,C being the angles of a triangle, Prove that *Image* ...

\hspace{-16}$Evaluate $\mathbf{\sum_{r=0}^{n-2}2^r.\tan \left(\frac{\pi}{2^{n-r}}\right)}\forall \mathbf{n\in \mathbb{Z}\geq 2}$ ...

\hspace{-16}$Let $\mathbf{P(x)}$ is a Quadratic in $\mathbf{x}$ Satisfying \\\\ $\mathbf{P(0)=\cos^3(40^0)\;, P(1)=\cos (40^0).\sin^2(40^0)\;,P(2)=0}$\\\\ Then $\mathbf{P(3)=}$ ...

\hspace{-16}$The Solution of the Inequality\\\\ $\mathbf{(\cot ^{-1}x).(\tan^{-1}x)+\left(2-\frac{\pi}{2}\right).\cot^{-1}x-3\tan^{-1}x-3.\left(2-\frac{\pi}{2}\right)>0}$ ...

\hspace{-16}$No. of Integral ordered pairs $\bf{(x,y)}$ satisfying the equation\\\\\\ $\bf{\tan^{-1}\left(\frac{1}{x}\right)+\tan^{-1}\left(\frac{1}{y}\right)=\tan^{-1}\left(\frac{1}{10}\right)}$ ...

\hspace{-16}\bf{\tan(1^{0})}$ is $\bf{\mathbb{R}}$ational or $\bf{\mathbb{I}}$rrational ...

If cosec-1x = 2 cot-12 + cos-1 (frac{3}{5}) , then x = ...

If x ≥ 1, then 2 tan -1x + sin-1 frac{2x}{1+{{x}^{2}}} is ...