Question

plz solve and give me ​

Answer 1

Answer:

(i) sin (A+B)= Sin A cos B + cos A sin B

sin (60+30)= Sin 60 cos 30 + cos 60 sin 30

sin 90°=√3/2 ×√3/2 +1/2 ×1/2

1=3/4 +1/4=4/4

1=1

(ii)cos(A+B)=cosA cosB-sinA sinB

cos(60+30)=cos60 cos30- sin60 sin30

cos90= 1/2×√3/2 -√3/2 ×1/2

0=√3/4 -√3/4

(iii)cos(A-B)=cosA cosB+sin A sinB

cos(60-30)=cos60 cos 30+sin 60 sin 30

cos 30=1/2×√3/2 +√3/2 ×1/2

√3/2 =√3/4+√3/4

√3/2=2√3/4

√3/2=√3/2

(iv)tan(A-B)=tan A-tan B/1+tanA×tan B

tan(60-30)=tan 60 - tan 30/1+tan 60×tan 30

tan 30=(√3- 1/√3)/(1+√3×1/√3)

1/√3=(3-1/√3)/(1+1)

1/√3=(2/√3)/2

1/√3=1/√3