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# In triangle ABC find value of cos(A-B)-cos(C) in terms of sin and cos

Arun
25763 Points
3 years ago
We have :  Cos ( A - B ) -  Cos C  and angle are from triangle ABC we know from angle sum property of triangle in triangle ABC :
A + B + C  =  180° ,
C = 180° - ( A + B )  , Substitute in given equation we get
Cos ( A - B ) -  Cos [ 180° - ( A + B ) ]
Cos ( A - B ) - [- Cos ( A + B ) ]   ( We know Cos ( 180° - θ ) = - Cos θ )
Cos ( A - B )  +  Cos ( A + B )

We know : Cos ( A - B ) = Cos A Cos B +  Sin A  Sin B  and  Cos ( A + B ) = Cos A Cos B - Sin A Sin B , So

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

Cos A Cos B +  Sin A  Sin B + Cos A Cos B - Sin A Sin B

2 Cos A Cos B  ( Ans )

We can't solve it further as we do not have any information regarding nature of triangle ABC . So kindly recheck your query and get back to us if above solution is not given you , yours required answer .