Chapter1 (Q4) Find Cos ( x+t) and cos ( x-t).a.Sinx=2/3 and sint=-1/3,x in quadrant 2and t quadrant 4b.Sinx=√5/7 and sint=√6/8,x in and t inquadrant 1c.Cosx=√2/4 and sint=-√5/6,x and t in quadrant 4

Solution

a. \(Cosx=√(1-sin^2 ) x←√(1-(4/9))=-√5/3

Cost=√(1-sin^2 ) t←√(1-(1/9))=√8/9

Cos (x+t)=Cosxcost+Sinxsint

Cos (x+t)=-√5/3×√8/9-2/3×(-1/3)=(-√40)/27+2/9=(-√(40 )+6)/27.

Cos (x-t)=-√5/3×√8/3+2/3×(-1/3)=(-√40)/9-2/9 \)=

b. \(Cosx=√(1-sin^2 ) x←√(1-(5/49))=√44/7

Cost=√(1-sin^2 ) t←√(1-(6/64))=√58/8

Cos (x+t)=Cosxcost+Sinxsint

Cos (x+t)=√44/7×√58/8-√5/7×(√6/8)=√2552/56+√30/56 \)=

Cos (x-t)=√44/7×√58/8+√5/7×(√6/8)=√2552/56-√30/56 \)=

c. \(Sinx=√(1-cos^2 ) x←√(1-(2/16))=-√14/4

cost=√(1-sin^2 ) x←√(1-(5/36))=√29/6

Cos (x+t)=Cosxcost-Sinxsint

Cos (x+t)=√2/4×√29/6 -(-√14/4 )×(√5/6)=√58/24+√70/24=(√(58 )+√70)/24.

Cos (x-t)=√2/4×√29/6+(-√14/4 )×(√5/6)=√58/24-√70/24 \)=

a. Cos (x-t)=-√5/3×√8/3+2/3×(-1/3)=(-√40)/9-2/9=(-√(40 )-6)/9.

b. Cos (x-t)=√44/7×√58/8+√5/7×(√6/8)=√2552/56-√30/56=(√(2552 )-√30)/56.

c. Cos (x-t)=√2/4×√29/6+(-√14/4)×(√5/6)=√58/24-√70/24=(√(58 )-√70)/24.