Questions in trigonometry

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The sides of a triangle are 4, 5 and 6cm. The area of the triangle is equal to
If $\alpha ,\beta ,\gamma $ are angles of a triangle, then ${{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma -2\cos \alpha \cos \beta \cos \gamma $ is
If in $\Delta ABC,$ $a=6,b=3$ and $\cos (A-B)=\frac{4}{5}$ , then its area will be
In $\Delta ABC$ , if $2s=a+b+c$ , then the value of $\frac{s(s-a)}{bc}-\frac{(s-b)(s-c)}{bc}=$
In $\Delta ABC$ if $a=2,b=4$ and $\angle C={{60}^{o}}$ , then $\angle A$ and $\angle B$ are equal to
The area of a $\Delta ABC$ is equal to
If in triangle $ABC,\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}=\frac{\sin (A-B)}{\sin (A+B)}$ , then the triangle is
In a triangle $ABC$ , sin$A:\sin B$ : $\sin C=1:2:3$. If $b=4$ cm, the perimeter of the triangle is
The ratios of the sides in a triangle are 5: 12: 13 and its area is 270 square cm. The sides of the triangle in cm are
If in triangle $ABC,\cos A=\frac{\sin B}{2\sin C}$ , then the triangle is

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