Without using trigonometric tables, find the value of: 4 ( ^4 30^…

Find the value of $x$ in the following: $\sqrt{3} \tan 2 x=\cos 60^{\circ}+\sin 45^{\circ} \cos 45^{\circ}$

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Construct an equilateral triangle using the given data: Altitude $OM = 5.8 \ cm$

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Find the logarithm of : $0.001$ to the base $10$

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In $\triangle ABC, D$ is the mid$-$point of $AB$ and $E$ is the mid$-$point of $BC.$

Calculate:
$(i) DE,$ if $AC = 8.6 \ cm$
$(ii) \angle DEB,$ if $\angle ACB = 72^\circ $

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The mean age of a group of 40 students is 17.45 years. Find the missing frequencies.

Age (in years)	15	16	17	18	19	20
Number of students	3	?	9	11	?	3

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If $\log 8=0.90$, find the value of each of the following: $\log \sqrt{32}$

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The following figure shows a trapezium $ABCD$ in which $AB \| DC$. $P$ is the mid$-$point of $AD$ and $PR\| AB$. Prove that:$PR=\frac{1}{2}(AB+CD)$

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In $\triangle ABC, AD$ is a median. The perpendiculars from $B$ and $C$ meet the line $AD$ produced at $X$ and $Y$. Prove that $BX = CY.$

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Three cubes, whose edges are $x \ cm, 8 \ cm$, and $10 \ cm$ respectively, are melted and recast into a single cube of edge $12 \ cm$. Find $'x'.$

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Solve for $x : \frac{\log 125}{\log 5}=\log x$

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Answer