Class 11MathematicsTrigonometrical EquationsMix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance
EasyIn a $\triangle ABC$,if $a \cos^2 \frac{C}{2} + c \cos^2 \frac{A}{2} = \frac{3b}{2}$,then
- A$2b = a + c$
- B$b^2 = ac$
- C$b^2 = \frac{2ac}{a+c}$
- D$a + b + c = 1$
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Easy
View SolutionMatch the items of List-$I$ with those of List-$II$ (Here $\Delta$ denotes the area of $\triangle ABC$.)
List-$I$ List-$II$ $(A)$ $\sum \cot A$ $(i)$ $\frac{(a+b+c)^2}{4\Delta}$ $(B)$ $\sum \cot \frac{A}{2}$ $(ii)$ $\frac{a^2+b^2+c^2}{4\Delta}$ $(C)$ If $\tan A : \tan B : \tan C = 1 : 2 : 3$,then $\sin A : \sin B : \sin C =$ $(iii)$ $8 : 6 : 5$ $(D)$ If $\cot \frac{A}{2} : \cot \frac{B}{2} : \cot \frac{C}{2} = 3 : 7 : 9$,then $a : b : c =$ $(iv)$ $12 : 5 : 13$ $(v)$ $\sqrt{5} : 2\sqrt{2} : 3$ $(vi)$ $4\Delta$
Then the correct match is
| List-$I$ | List-$II$ |
| $(A)$ $\sum \cot A$ | $(i)$ $\frac{(a+b+c)^2}{4\Delta}$ |
| $(B)$ $\sum \cot \frac{A}{2}$ | $(ii)$ $\frac{a^2+b^2+c^2}{4\Delta}$ |
| $(C)$ If $\tan A : \tan B : \tan C = 1 : 2 : 3$,then $\sin A : \sin B : \sin C =$ | $(iii)$ $8 : 6 : 5$ |
| $(D)$ If $\cot \frac{A}{2} : \cot \frac{B}{2} : \cot \frac{C}{2} = 3 : 7 : 9$,then $a : b : c =$ | $(iv)$ $12 : 5 : 13$ |
| $(v)$ $\sqrt{5} : 2\sqrt{2} : 3$ | |
| $(vi)$ $4\Delta$ |
Then the correct match is
DifficultAP EAMCET 2024
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