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# Tag Archives: General

## Trigonometric inequality on an acute triangle

Prove that in any acute triangle the following inequality holds:

**Solution**

## Equality on a triangle

Let be a triangle. Show that

**Solution**

Let denote the semiperimeter of the triangle. On account of the well known relations,

(1)

(2)

we have:

## On the geometrical view of an integral

Evaluate the integral

using geometric methods.

**Solution**

We are working on the following figure

Thus,

since the red angle is due to the triangle since ( ). Therefore , the green angle is . Finally, the area of the circular sector is equal to

where and .

## Trigonometric sum

Prove that

**Solution**