Question

tan A + tan B.
1-tanA.tanB
sinA=1/√2 cos B=√3/2​

Answer 1

$sina = \frac{1}{ \sqrt{2} } ;∴a = 45 \\ cosb = \frac{ \sqrt{3} }{2} ;∴b = 30$

Thus,

$(tana + tanb)(1 - tana \times tanb) \\ = (tan45 + tan30)(1 - tan45 \times tan30) \\ = (1 + \frac{1}{ \sqrt{3} } )(1 - 1 \times \frac{1}{ \sqrt{3} } ) \\ = ( \frac{ \sqrt{3} + 1) }{ \sqrt{3} } )(1 - \frac{1}{ \sqrt{3} } ) \\ = \frac{( \sqrt{3} + 1)( \sqrt{3} - 1)}{ \sqrt{3} \times \sqrt{3} } \\ = \frac{ {( \sqrt{3} )}^{2} - {(1)}^{2} }{3} = \frac{3 - 1}{3} = \frac{2}{3}$