JEE Main · 2006 · 30 Apr 2006 · Offline · Trigonometric Ratios and Identities

More JEE Main questions on Trigonometric Ratios and Identities

1. The value of $\mathrm{cosec}10^{\circ }-\sqrt{3}\sec 10^{\circ }$ is equal to:
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2. If $\frac{{\cos }^{2}48^{\circ }-{\sin }^{2}12^{\circ }}{{\sin }^{2}24^{\circ }-{\sin }^2{6}^{\circ }}=\frac{\alpha +\beta \sqrt{5}}{2}$, where $\alpha ,\beta \in \mathbb{N}$, then $\alpha +\beta$ is equal to
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3. Let $\cos (\alpha +\beta )=-\frac{1}{10}$ and $\sin (\alpha -\beta )=\frac{3}{8}$, where $0<\alpha <\frac{\pi }{3}$ and $0<\beta <\frac{\pi }{4}$.
   
   If $\tan 2\alpha =\frac{3(1-r\sqrt{5})}{\sqrt{11}(s+\sqrt{5})},r,s\in \mathbb{N}$, then $r+s$ is equal to ______。
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4. Let $\alpha$ and $\beta$ respectively be the maximum and the minimum values of the function …
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5. Let $\frac{\pi }{2}<\theta <\pi$ and $\cot \theta =-\frac{1}{2\sqrt{2}}$. Then the value of $\sin \left(\frac{15\theta }{2}\right)(\cos 8\theta +\sin 8\theta )+\cos \left(\frac{15\theta }{2}\right)(\cos 8\theta -\sin 8\theta )$ is equal to :
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6. The least value of $\left({\cos }^2\theta -6\sin \theta \cos \theta +3{\sin }^2\theta +2\right)$ is
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