Class 11MathematicsTrigonometrical EquationsMix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance
MediumIf $A, B, C$ are the angles of a triangle,then $\sin^2 A + \sin^2 B + \sin^2 C - 2\cos A \cos B \cos C = $
- A$1$
- B$2$
- C$3$
- D$4$
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Let $S=\{x \in(-\pi, \pi) \mid x \neq 0, \pm \frac{\pi}{2}\}$. The sum of all distinct solutions of the equation $\sqrt{3} \sec x+\operatorname{cosec} x+2(\tan x-\cot x)=0$ in the set $S$ is equal to
DifficultIIT 2016
View SolutionIn $\triangle ABC$,if $a=2$,$B=\tan ^{-1} \frac{1}{2}$ and $C=\tan ^{-1} \frac{1}{3}$,then $(A, b)$ equals
MediumKCET 2010
View SolutionThe smallest positive root of the equation $\tan x - x = 0$ lies in the interval
In $\triangle ABC$,if $3 \sin A + 4 \cos B = 6$ and $4 \sin B + 3 \cos A = 1$,then the $\angle C$ is
If triangle $ABC$ is right-angled at $A$ and $\tan \frac{B}{2}, \tan \frac{C}{2}$ are roots of the equation $ax^2 + bx + c = 0$ $(a \neq 0)$,then:
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