Question

value of A if tanA = 2 +√3

Answer 1

$\huge\mathfrak\red{Answer}$

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TRIGONOMETRIC

FUNCTIONS......

$tan \alpha = 2 + \sqrt{3} \\ \\ multiply \: and \: divide \: by \: 2 \\ \\ \tan \alpha = \frac{4 + 2 \sqrt{3} }{2} \\ \tan \alpha = \frac{ {(1)}^{2} + ( { \sqrt{3} })^{2} + 2 \times \sqrt{3} }{( { \sqrt{3} })^{2} - ({1}^{2} ) } \\ \\ \tan \alpha = \frac{ {(1 + \sqrt{3} } )^{2} }{( \sqrt{3} + 1)( \sqrt{3 } - 1) } \\ \\ \tan \alpha = \frac{1 + \sqrt{3} }{ \sqrt{3} - 1} \\ \\ take \: \sqrt{3} \: common \\ \\ \tan \alpha = \frac{ \sqrt{3}( \frac{1}{ \sqrt{3} } + 1 )}{ \sqrt{3} (1 - \frac{1}{ \sqrt{3} }) } \\ \\ finlly \: we \: get \\ \\ \tan \alpha = \frac{1 + \frac{1}{ \sqrt{3} } }{1 - \frac{1}{ \sqrt{3} } } \\ \\ \tan \alpha = \frac{ \tan45 + \tan30 }{1 - ( \tan45)( \tan30) } \\ \\ tan \alpha = \tan(45 + 30) \\ \\ tan \alpha = \tan75 \\ \\ \alpha = 75$

WHEN YOU ARE DEALING WITH TANGENT FUNCTION THEN PLEASE TRY TO CONVERT THE FUNCTION IN SINE OR COS OR CONVERT IT INTO ADDITION PROPERTIES OR FORMULA OF TANGENT.