# If in a triangle ABC, #sinAsinB+cosAcosBsinC=1# then how will you prove that the triangle is right angled and isosceles?

##### 1 Answer

Feb 18, 2017

#### Answer:

The triangle is an isosceles and right angled triangle. See proof below.

#### Explanation:

As

i.e.

i.e.

Now the sum of the three terms on LHS will be

- (the latter is true as
#cosA# and#cosB# cannot be#0# )

Hence

Hence the triangle is an isosceles and right angled triangle.