JEE Advanced · 2009 · 12 Apr 2009 · Paper 1 · Trigonometric Ratios and Identities

More JEE Advanced questions on Trigonometric Ratios and Identities

1. Let
   

   $$\alpha =\frac{1}{\sin 60^{\circ }\sin 61^{\circ }}+\frac{1}{\sin 62^{\circ }\sin 63^{\circ }}+\dots +\frac{1}{\sin 118^{\circ }\sin 119^{\circ }}.$$

   
   Then the value of
   

   $${\left(\frac{\mathrm{cosec}{1}^{\mathrm{o}}}{\alpha }\right)}^2$$

   
   is ____.
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2. Let $\frac{\pi }{2}<\mathrm{x}<\pi$ be such that $\cot \mathrm{x}=\frac{-5}{\sqrt{11}}$. Then
   $\left(\sin \frac{11x}{2}\right)(\sin 6x-\cos 6x)+\left(\cos \frac{11x}{2}\right)(\sin 6x+\cos 6x)$ is equal to :
   JEE Advanced 2024 Copy linkView solution →
3. Let $\alpha$ and $\beta$ be real numbers such that $-\frac{\pi }{4}<\beta <0<\alpha <\frac{\pi }{4}$. If $\sin (\alpha +\beta )=\frac{1}{3}$ and $\cos (\alpha -\beta )=\frac{2}{3}$, then the greatest integer less than or equal to …
   JEE Advanced 2022 Copy linkView solution →
4. For non-negative integers n, let
   

   $$f(n)=\frac{{\sum }_{k=0}^n\sin \left(\frac{k+1}{n+2}\pi \right)\sin \left(\frac{k+2}{n+2}\pi \right)}{{\sum }_{k=0}^n{\sin }^2\left(\frac{k+1}{n+2}\pi \right)}$$

   
   Assuming ${\cos }^{-1}\mathrm{x}$ takes values in $[0,\pi ]$, which of the foll …
   JEE Advanced 2019 Copy linkView solution →
5. The value of ${\sec }^{-1}\left(\frac{1}{4}{\sum }_{\mathrm{k}=0}^{10}\sec \left(\frac{7\pi }{12}+\frac{\mathrm{k}\pi }{2}\right)\sec \left(\frac{7\pi }{12}+\frac{(\mathrm{k}+1)\pi }{2}\right)\right)$ in the interval $\left[-\frac{\pi }{4},\frac{3\pi }{4}\right]$ equals
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6. Let $\alpha$ and $\beta$ be nonzero real numbers such that $2(\cos \beta -\cos \alpha )+\cos \alpha \cos \beta =1$. Then which of the following is/are true?
   JEE Advanced 2017 Copy linkView solution →