Question

(i)
cos (A -B)_cot A.cot B+1
cos (A +B) cot A.cot B-1​

Answer 1

cos (A-B)= Cos A.Cos B+Sin A.Sin B

= (Cot A.SinA).(Cot B .SinB) + Sin A. Sin B

= Sin A. Sin B(Cot A.Cot B +1).................1.

Cos (A+B)=Cos A. Cos B- Sin A. Sin B

= Sin A.SinB( Cot A.Cot B-1)....................2.

Divide Eq. 1 and 2. you will get easily the derivation of the proof and thus proved.