`cos A . cos B -sin B. sin A =?`

Prove that : (sin A - sin B)/ (cos A + cos B) + (cos A - cos B)/ (sin A + sin B) = 0

If A = 60 ^(@) and B = 30 ^(@) , find the value of (sin A cos B+ cos A sin B)^(2) + (cos A cos B - sin A sin B )^(2)

Prove that ((cos A + cos B)/( sin A - sin B )) ^(n) + ((sin A + sin B )/( cos A - cos B )) ^(n) ={{:(2 cot ^(n) ((A- B)/(2)),"," "if n is even."),(0,",""if n is odd."):}.

In a triangle ABC , if cos A cos B + sin A sin B sin C = 1 , then a:b:c is equal to

If tan A =1 and tan b = sqrt3 , evaluate : cos A cos B - sin A sin B.

If = 60^(@) and B=30^(@) , then show that : sin A cos B+ cos A sin B= sin (A+B)

In any triangle ABC, if (cos A + 2 cos C)/(cos A + 2 cos B) = (sin B)/(sin C) then prove that, the triangle is either isosceles or right angled.

If A+B+C=180^0,\ then s e c A(cos B cos C-sin B sin C) is equal to:

Prove that (cos A - cos B) ^(2) + (sin A - sin B ) ^(2) = 4 sin ^(2) ((A -B)/( 2 )).

Prove that (cos A + cos B ) ^(2) +(sin A + sin B) ^(2) = 4 cos ^(2) ((A -B)/(2)).