In any ΔABC, prove that

a(b cos C – c cos B) = (b² – c²)

In any ΔABC, prove that

ac cos B – bc cos A = (a² – b²)

In any ΔABC, prove that

In any ΔABC, prove that

In any ΔABC, prove that

2(bc cos A + ca cos B + ab cos C) = (a² + b² + c²)

In any ΔABC, prove that

In any ΔABC, prove that

a sin A – b sin B = c sin (A – B)

In any ΔABC, prove that

a² sin ( B – C ) = (b² – c²) sin A

In any ΔABC, prove that

In any ΔABC, prove that

In any ΔABC, prove that

In any ΔABC, prove that

In any ΔABC, prove that

a²(cos²B – cos²C) + b²(cos²C – cos²A) + c²(cos²A – cos²B) = 0

In any ΔABC, prove that

In any ΔABC, prove that

In any ΔABC, prove that

(c² – a² + b²) tan A = (a² – b² + c²) tan B = (b² – c² + a²) tan C

If in a ∆ABC, ∠C = 90⁰, then prove that .

In a ∆ABC, if , show that the triangle is isosceles.

In a ∆ABC, if , show that the triangle is right-angled.

Solve the triangle in which a = 2 cm, b = 1 cm and c = cm.

In a ΔABC, if a = 3 cm, b = 5 cm and c = 7 cm, find cos A, cos B, cos C.

If the angles of a triangle are in the ratio 1 : 2 : 3, prove that its corresponding sides are in the ratio .

Two boats leave a port at the same time. One travels 60 km in the direction N 50⁰ E while the other travels 50 km in the direction S 70⁰ E. What is the distance between the boats?

A town B is 12 km south and 18 km west of a town A. Show that the bearing of B from A is S 56⁰ 20’ W. Also, find the distance of B from A.

At the foot of a mountain, the angle of elevation of its summit is 45⁰. After ascending 1 km towards the mountain up an incline of 30⁰, the elevation changes to 60⁰ (as shown in the given figure). Find the height of the mountain. [Given : ]