goals

Form the pair of linear equations for the following problems and find their solution by the substitution method.

The larger of two supplementary angles exceeds the smaller by $$18$$ degrees. Find them

The larger of two supplementary angles exceeds the smaller by $$18$$ degrees. Find them

In a $$\triangle ABC,$$ right angled at $$A$$. The radius of the inscribed circle is $$2$$cm.Radius of the circle touching the side $$BC$$ and also sides $$AB$$ and $$AC$$ produced is $$15$$cm.The length of the side $$BC$$ measured in cm is

The altitude of a triangle is two-third the length of its corresponding base. If the altitude is increased by 4 cm and the base is decreased by 2 cm ,the area of the triangle remains the same. Find the base and the altitude of the triangle.

In any $$\triangle ABC, \dfrac{\cos{2A}}{{a}^{2}}-\dfrac{\cos{2B}}{{b}^{2}}$$ is independent of the measures of the angles $$A$$ and $$B$$

For any $$\triangle ABC$$,

$$\cos^{2}\left(\dfrac {A}{2}\right) + \cos^{2}\left(\dfrac {B}{2}\right)+ \cos^{2}\left(\dfrac {C}{2}\right)=2\sin\left(\dfrac {A}{2}\right) 2+2\sin\left(\dfrac {B}{2}\right) \sin\left(\dfrac {C}{2}\right)$$

$$\cos^{2}\left(\dfrac {A}{2}\right) + \cos^{2}\left(\dfrac {B}{2}\right)+ \cos^{2}\left(\dfrac {C}{2}\right)=2\sin\left(\dfrac {A}{2}\right) 2+2\sin\left(\dfrac {B}{2}\right) \sin\left(\dfrac {C}{2}\right)$$