Question

$If \: sin \: A \: = \: \frac{ \sqrt{3} }{2} \: and \: cos \: B \: = \: \frac{ \sqrt{3} }{2} , \\ \: find \: the \: value \: of \: : \: \frac{tan A - tan B}{1 + tan A \: tan B}$
✔️✔️Need explained answers only
✔️✔️ No plagiarism
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Answer 1

Answer:

1/root3

Step-by-step explanation:

SinA = root3/2

CosA = root( 1 - sin²A) = root(1- 3/4) = root(1/4) = 1/2

TanA = SinA/CosA = root3

Cos B = Sin(90°-B) = root3/2 = sinA

=> 90° - B = A

=> A+B = 90°

TanB = Tan(90°-A) = CotA = 1/TanA = 1/root3

Therefore,

(TanA - TanB)/1+TanA×TanB

= (root3 - 1/root3)/1 + root3×1/root3

= ( 3-1)/2×root3 = 1/root3

Answer 2

Sin =3/5=B/AC

Co3A =3110/sin =AB /AC 45/5

tana =sin/3110 =BC /AB =3/1