Question

1 +tan 75/1-tan75 solve the qno​

Answer 1

SOLUTION

TO DETERMINE

$\displaystyle \sf{ \frac{1 + \tan {75 }^{ \circ} }{1 - \tan {75 }^{ \circ} } }$

FORMULA TO BE IMPLEMENTED

$\displaystyle \sf{ \tan ( \alpha + \beta ) = \frac{ \tan \alpha + \tan \beta }{1 - \tan \alpha \tan \beta } }$

EVALUATION

$\displaystyle \sf{ \frac{1 + \tan {75 }^{ \circ} }{1 - \tan {75 }^{ \circ} } }$

$\displaystyle \sf{ = \frac{ \tan {45 }^{ \circ}+ \tan {75 }^{ \circ} }{1 - \tan {45 }^{ \circ} \tan {75 }^{ \circ} } }$

$\displaystyle \sf{ = \tan( {45 }^{ \circ}+ {75 }^{ \circ}) }$

$\displaystyle \sf{ = \tan {120 }^{ \circ}}$

$\displaystyle \sf{ = - \tan {60 }^{ \circ}}$

$\displaystyle \sf{ = - \sqrt{3} }$

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