1 If sin u 1 cos v and u v in Q1 find cos u v Sam ond dit e

1.) If sin u 1, cos v and u & v in Q1, find cos (u v) Sam ond dit eni ,dent tes for Co Sine sin (v) 2.) If sin u COS v and u & v in Q1, find tan (u Sam and difference denkhz. Tangent use this u) tan len)- tan (v) tan (a) tan (U

Solution

1)sinu =opposite side/hypotenuse= 4/5

by pythogorus theorem

hypotenuse²=opposite side²+ adjacent side²

5²=4²+ adjacent side²

adjacent side²=9

adjacent side=3

cosu =adjacent side/hypotenuse= 3/5

cosv =adjacent side/hypotenuse= 5/13

13²=opposite side²+ 5²

opposite side²=144

opposite side=12

sinv =opposite side/hypotenuse= 12/13

cos(u+v) =cosucosv -sinusinv

cos(u+v)=((3_/5)(5_/13))-((4_/5)(12_/13))

cos(u+v)=(15-48)_/65

cos(u+v)=-33_/65

2)

tanu=opposite side/adjacent side=4/3

tanv=opposite side/adjacent side=12/5

tan(u-v)=[tanv-tanv]_{/[1+tanutanv]}

tan(u-v)=[(12/5)-(4/3)]_{/[1+ (4/3)(12/5)]}

tan(u-v)=(36-20)_{/[15+ 48]}

tan(u-v)=16_/63

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1)sinxcosx(tanx +cotx)

=sinxcosx((sinx_/cosx) +(cosx_/sinx))

=sin²x+cos²x

=1