Question

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Answer 1

sinA=35, A lies in 1st quadrant.

∴cos2A=1-sin2A=1-(35)2=1625

⇒cosA=45

and tanA=sinAcosA=3545=34

Again cosB=-1213, B lies in 3rd quadrant.

∴sin2B=-513 (In 3rd quadrant, sin is negative)

∴tanB=sinBcosB=-513-1213=512

i) sin(A-B)=sinAcosB-cosAsinB

=35(-1213)-45(-513)

=-36+2065=-1665. Ans.

ii) cos(A-B)=cosA.cosB+sinAsinB

=45(-1213)+35(-513)

=-48-1565=-6365 Ans.

iii) tan(A+B)=tanA+tanB1-tanAtanB

=34+5121-34.512=5633. Ans.

Answer 2

x belongs to [3,6]

x =whole number

x belongs to [3,w]

w is >6

w=6

w>3 and w<6

w is > X,x is >3 and x is <6

Therefore,X={3,4,5,6}

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