1.

Given that

=

, prove that cos A cos B = 6 sin A sin B

Mr F says: Substitute from the appropriate double angle formula in the numerator and denominator, cross multiply to get rid of fractions, and simplify.
and deduce a relationship between tan A and tan B.

Mr F says: Divide both sides of cos A cos B = 6 sin A sin B by cos A cos B .....
Given further that A+B=

, calculate the value of tan A + tan B.

Mr F says: . And from the previous result you know what tan A tan B is equal to.
2.

If A, B and C are the angles of a triangle, prove that sin A - sin(B+C)=0.

Mr F says: Here's a start: ......
Hence, prove that sin A - sin(B-C)= 2 cos B sin C .

Mr F says: It's not difficult to use the compound angle formulae to show that sin (B + C) = sin (B - C) + 2 sin C cos B ......