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Question

If A=B=60, verify that
(i) cos(AB)=cosAcosB+sinAsinB
(ii) sin(AB)=sinAcosBcosAsinB
(iii) tan(AB)=tanAtanB1+tanAtanB

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Solution

A=B=60

we know that

sin60=32,sin30=12

(i) cos(AB)=cosAcosB+sinAsinB
cos(6060)=cos60cos60+sin60sin60
cos(0)=cos260+sin260

1=(12)2+(32)2

1=(14)+(34)

1=44

1=1

Hence verified

(ii) sin(AB)=sinAcosBcosAsinB
sin(6060)=sin60cos60cos60sin60

sin(0)=(32×12) (12×32)

0=3434

0=0

Hence verified

(iii) tan(AB)=tanAtanB1+tanAtanB

tan(6060)=tan60tan601+tan60tan60

tan(0)=01+tan60tan60

0=0

Hence verified

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