Question

if tan (A + B) is not defined and Sin (A -B)=1/2 where a and b are acute angles then evaluate (i) cos A.cos B + sinA.sinB
(ii) tanA-tanB
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1+tanA.tanB

Answer 1

Sin(A-B)=1/2

Sin(A-B)=sin30°

A-B=30° is 1st equation

A+B+C=180°

A+B=180°-90°

A+B=90° is 2nd equation

Subtract equation 1st from 2nd,we get

2B=60°

B=30°

Put B=30°in equation 1st

A-30=30

A=60

CosA.cosB+sinA.sinB=

=cos60°×cos30°+sin60°×sin30°

=1/2×√3/2+√3/2×1/2

=√3/4+√3/4 =2√3/4 =√3/2

TanA-TanB=tan60°-tan30° =√3-1/√3

=√3/√3-1/√3=1/√3

Answer 2

Explanation:

1 s t a n s w e r I s. r I g h t s o p l s l I k e m y a n s