Recently Active Trignometry Questions

If \sqrt {a+b} \tan \frac {\theta}{2}=\sqrt {a-b} \tan \frac {\phi}{2} then prove that (b-a\ sec \theta)(b+a\cos \phi)\leq 0 ...

in a triangle,R=2r then the triangle is a)right angle b)isosceles c)equilateral d)none ...

2sin45/4°=√2-√2+√2 prove this ? ( the first root is the main root.the second and the third root is under the main root). ...

Solve \left|\sin x\right|^{\sin ^2x-\sin x-2 }<1 ...

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

if α lies in the fourth quadrant and cosα=3/7 find the values of sinα/2 and cosα/2 ? ...

1)Evaluate \sum_{0}^{infinity}{sin(n\alpha )/n} = ??? (n varies from 0 to infinity) [\alpha\varepsilon (0,2\pi )] 2)Find the sum of \sum_{r=00}^{infity}{\frac{sinr\alpha }{sin^{r}\alpha }} ...

if....\theta =\frac{2\pi }{2009}.... then.....cos\theta cos 2\theta cos 3\theta ..............cos 1004\theta ........is equal to ..... ...

if x,y,z are real numbers satisfying the relations \[ x+y+z = 1\quad\textrm{and}\quad\arctan x+\arctan y+\arctan z =\frac{\pi}{4}, \] prove that $ x^{2n+1}+y^{2n+1}+z^{2n+1}= 1 $ holds true for all positive integers n . ...

7)sin x<1/2 ½=sin 30 =sin(180-30)=sin 150 or, sin30<1/2 and sin 150 >1/2(why? And how?) or, x belongs to (0,30) union (150,360) [given: 0<x<360] I want a complete explanation. 8) Give the general soln of x: lo ...

Reduce to simplest form tan^{-1}(\frac {xcos\theta}{1-xsin\theta})-cot^{-1}(\frac {cos\theta}{x-sin\theta}) ...

If x=cosec(tan-1(cos(cot-1(sec(sin-1a))))) and y=sec(cot-1(sin(tan-1(cosec(cos-1a))))) where 0≤a≤1.Find relationship between x and y ...

Find the roots of x^2+(4x^3-3x)^2=1 ...

\\x_1-1/x_1=2x_2 \\x_2-1/x_2=2x_3 \\x_3-1/x_3=2x_4 \\x_4-1/x_4=2x_1 Solve this set of equations.. ...

Q1 If cos-1λ +cos-1μ +cos-1ν=3π then prove that λμ+μν+λν=3 Q2 If 2nΣi=1 sin-1xi=nπ then prove that 2nΣi=1xi=2n ...

*Image* Q3 *Image* ...

If Σsin-1x=π,then prove that x4+y4+z4+4x2y2z2=2(x2y2+y2z2+z2x2) ...

Just saw this problem in some Coaching Institute material. If cos A + cos B + cos C = sin A + sin B + sin C = 0, prove that cos (A-B) + cos (B-C) + cos (C-A) = -3/2 ...

errr....just got confused...which one of these is correct?? sin(a) + sin(a+d) + sin(a+2d) + sin(a+3d) + ...... + sin(a+nd) = \frac{sin\left(\frac{2a+nd}{2}\right)sin\left(\frac{nd}{2} \right)}{sin\left(\frac{d}{2} \right)} OR ...

In a triangle ABC , find the least value of, cot A/2 * cot B/2 * cot C/2 * cos A/2 * cos B/2 * cos C/2 ...

show that the equation secθ + cosecθ = c has two solutions between 0 and 2π if c2 < 8 and four solutions if c2 > 8. I've tried but didn't get the correct answer. ...

Please explain this question, how the solution has been obtained? *Image* ...

1) If sin x + sin y = 3(cos y - cos x), then find the value of sin3x + sin3y ? 2) If sin (x/2) + cos (x/2) = -1/2 , 3pie/2 < x < 2pie, then the value of sin2x? ...

(1) find value of x in cos7x+sin4x = 1 ...

solve cos2x-sinx=0 ...

evaluate: ∞ Σn=1(sin(nθ))/n ...

solve the following: tanx-sinx=\frac{x^{3}}{2} ...

find (p) so that the given equation has real solutions (cos p -1)x2 + (cos p)x + sin p =0 ...

1+ \frac{cos\theta }{cos\theta } + \frac{cos2\theta }{cos^2\theta } + \frac{cos3\theta }{cos^3\theta } + ... upto \infty for those whose latex is not working 1+ cosθ/cosθ + cos2θ/cos2θ + cos3θ/cos3θ + ... upto ∞ ...

Prove that tan-1( 1+x - 1-x )/( 1+x + 1-x ) = π/4-1/2 Cos-1x 0<x<1. ...