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

##### 2 Answers

#### Answer:

Please see below.

#### Explanation:

Multiplying both sides by

or

or

Note that all three terms contained above are positive, as while first two terms are squares and hence positive, third term is positive as sine of angles

But, their sum is zero and hence each term is equal to zero, i.e.

i.e.

Hence the triangle is isosceles and right angled.

#### Answer:

as follows

#### Explanation:

Given

Now in above relation the first term being squared quantity will be positive.In the second term A,B and C all are less than

So sinA ,sinB and sinC all are positive and less than 1.So the 2nd term as a whole is positive.

But RHS=0.

It is only possible iff each term becomes zero.

When

then

and when 2nd term=0 then

0< A and B <180

So

So in triangle ABC