prove the following : 1 ) cos ( A-B ) cot A cot B +1 - Economics - Introduction to Macro Economics

Question

prove the following :
1 ) cos ( A-B ) cot A cot B +1
=
cos ( A +B ) cot A cot B - 1
2 ) sin ( A-B ) sin ( B-C )
+
sin A sin B sin B sin C

Varun.Rawat · Accepted Answer

Dear Student,

Please find below the solution to the asked query :

1 LHS = cosA-BcosA+B=cos A 
 cos B + sin A 
 sin Bcos A 
 cos B - sin A 
 sin B=cos A   cos Bsin A 
 sin B + sin A 
 sin Bsin A   sin Bcos A 
 cos Bsin A 
 sin B - sin A 
 sin Bsin A   sin B=cot A 
 cot B + 1cot A 
 cot B - 1=RHS2 sinA-Bsin A 
 sin B + sinB-Csin B 
 sin C=sin A 
 cos B - cos A 
 sin Bsin A 
 sin B + sin B 
 cos C - cos B 
 sin Csin B 
 sin C=cot B - cot A + cot C - cot B=cot C - cot A

Hope this information will clear your doubt about the topic

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prove the following : 1 ) cos ( A-B ) cot A.cot B +1 .................... = cos ( A +B ) cot A.cot B - 1 2 ) sin ( A-B ) sin ( B-C ) ................. + .................... sin A.sin B sin B . sin C

prove the following :
1 ) cos ( A-B ) cot A.cot B +1
.................... =
cos ( A +B ) cot A.cot B - 1
2 ) sin ( A-B ) sin ( B-C )
................. + ....................
sin A.sin B sin B . sin C