Sine and Cosine Rule

If $A=75°, B=45°$, then $b+c\sqrt{2}$ equals

The sides of a triangle are $a, b, \sqrt{a^2+b^2+ab}$. Then the greatest angle is

In the adjacent figure $AB$ is the diameter of circle, centered at ${}^{\text{'}}O^{\text{'}}$. If $\angle COA=60°, AB=2r, AC=d$ and $CD=\ell ,$ then

In a triangle $ABC, \frac{a\cos A+b\cos B+c\cos C}{a+b+c}$ is equal to

The perimeter of a $∆ABC$ is $6$ times the arithmetic mean of the sines of its angles. If the side $a$ is $1$, then the angle $A$ can be equal to

In a $\mathrm{\Delta }ABC, b=\sqrt{3}+1, c=\sqrt{3}-1, \angle A=60°$, then the value of $\tan \left(\frac{B-C}{2}\right)$ is

If the circle with altitude $AD$ of $\mathrm{\Delta }ABC$ as diameter intersect $AB$ and $AC$ at the point $E$ and $F$, then $EF$ is equal to

Let the angles $A, B, C$ of $∆ABC$ be in $\mathrm{AP}$ and let $b:c=\sqrt{3}:\sqrt{2}$. Then angle $A$ is

In any triangle $ABC$, $\left(b+c\right)\cos A+\left(c+a\right)\cos B+\left(a+b\right)\cos C$ equals

In any $∆ABC$, $2\left[a{\sin }^2\left(\frac{C}{2}\right)+c{\sin }^2\left(\frac{A}{2}\right)\right]$ equals

If ${\sin }^{2}A+{\sin }^{2}B={\sin }^{2}C,$ then the triangle is

The smallest angle of the triangle whose sides are $6+\sqrt{12}, \sqrt{48}, \sqrt{24}$ is

In a triangle $ABC$, if $a=2, B=60°$ and $C=75°,$ then $b$ equals

In a $∆ABC$, $a=2 \mathrm{cm}$, $b=3 \mathrm{cm}$, $c=4 \mathrm{cm}$, then $\cos A$ equals to