Recently Active Trignometry Questions

\hspace{-16}\mathbb{I}$f $\bf{n \; \mathbb{\in \mathbb{N}}}$. Then find value of $\bf{n}$ in \\\\ $\bf{\tan^{-1}\left(\frac{1}{11}\right)+n.\tan^{-1}\left(\frac{1}{7}\right)=\tan^{-1}\left(\frac{1}{n}\right)}$ ...

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

\hspace{-16}\bf{\lim_{n\rightarrow \infty}\frac{1}{n}\tan\left\{\sum_{k=1}^{4n+1}\tan^{-1}\left(1+\frac{2}{k.(k+1)}\right)\right\}=} ...

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

*Image* from goiit.com ...

\hspace{-16}$Calculate value of expression\\\\\\ $\bf{\sin\left(\tan^{-1}\left(\frac{1}{3}\right)+\tan^{-1}\left(\frac{1}{5}\right)+\tan^{-1}\left(\frac{1}{7}\right)+\tan^{-1}\left(\frac{1}{11}\right)+\tan^{-1}\left(\frac{1}{ ...

sum till infinite terms of the series cot-1 3 + cot-1 7 + cot-113 + ....... is (A) pi/2 (B) cot-1 1 (C) tan-1 2 (D) none of these my approach this is something we have to find *Image* now how to approach (2) sin-1 sin 12 + co ...

1)Find tan-1 1/x2+x+1 + tan-1 1/x2+3x+3 + tan-1 1/x2+5x+7 + tan-1 1/x2+7x+13 ..... upto n terms.... 2)If sin(cot-1(x+1))=cos(tan-1x),then x= ? 3) If \sum_{n=1}^{10}{}\sum_{m=1}^{10}{}tan^{-1}(\frac{m}{n})=k\pi\, then \: find ...

\hspace{-16}$Find all Real ordered pairs $\bf{(x,y,z)}$ in $\bf{\tan^2(x)+\cot^2(y)+\csc^2(z)=\frac{1}{2}}$ ...

\hspace{-16}$Find Sum of $\bf{\sec(40^{0})+\sec(80^{0})+\sec{160^0}=}$ ...

In triangle ABC if cotA =(x3+x3+x)1/2 , cotB = (x+x-1+1)1/2 and cotC=(x-3+x-2+x-1)1/2 then find the magnitude of angle C. ...

\hspace{-16}\bf{\sum_{n=1}^{\infty}\;\prod_{r=1}^{n}\cos \left(\frac{r\pi}{n}\right)} ...

\hspace{-16}\bf{P=\left(1+\frac{1}{\cos 1^0}\right).\left(1+\frac{1}{\cos 2^0}\right).\left(1+\frac{1}{\cos 4^0}\right)...\left(1+\frac{1}{\cos 1024^0}\right)} ...

\hspace{-16}$Let $\mathbf{A=\sin \sqrt{2}-\sin \sqrt{3}}$ and $\mathbf{B=\cos \sqrt{3}-\cos \sqrt{2}}$\\\\ Then Correct options is,::::\\\\ $\mathbf{(a)\;\; A>0\;\;,B>0}$\\\\ $\mathbf{(b)\;\; A>0\;\;,B<0}$\\\\ $\m ...

\hspace{-16}$If $\bf{\sin x.\cos x\leq \mathbb{C}\big(\sin^6x+\cos ^6x\big)}$. Then $\bf{\mathbb{C}}$ is ...

solve for least values x and y... 2(sin x + sin y) - 2 cos(x-y)=3. ...

If a , b and c are angles in triangle such cot a + cot b + cot c = √3 prove that abc is an equalitial triangle. ...

find the number of values of x at which the function y=cos x + cos √2x is maximum is? options 0 2 1 infinite ...

\hspace{-16}$Evaluate $\mathbf{\sum_{k=1}^n \left\{\tan (2)^{k-1}.\sec(2)^k\right\}=}$\\\\\\ Where $\mathbf{\left\{x\right\}\neq }$ a fractional part function. ...

ur approach...................?? q) In a triangle ABC, AC = BC then sin [ 3(A + B)/4 ] equals... i) Sin { B + 2C/2 } ii) Sin { A + 2C/2 } iii) Sin { B + 4C/2 } iv) Sin (B - 3C) ...

\hspace{-16}$If $\mathbf{\cos ^n(x)-\sin^{n}(x)=1}$ have $\mathbf{11}$ Roots in $\mathbf{\left[0,\frac{23\pi}{2}\right)}$. Then $\mathbf{n}$ can be ...

\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}$In $\mathbf{\left(0,\frac{\pi}{2}\right)},$ one Solution of $\mathbf{\frac{\sqrt{3}-1}{\sin x}+\frac{\sqrt{3}+1}{\cos x}=4\sqrt{2}}$\\\\\\ is $\frac{\pi}{12}$ and other solution is $\mathbf{\frac{\lambda.\pi}{36} ...

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

Show that: cos( π/7 )cos( 2π/7 )cos( 3π/7 )= 1/8 ...

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

what is the value of sincube.cos+coscube.sin will u please explain me with the help of a solution ...

given for angles A1,A2,A3 ΣcosA = ΣsinA = 0 prove that 1)Σcos2A = Σsin2A = 0 2)Σcos2A = Σsin2A = 3/2 ...

\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}+ ...