Question

8f x=45 ‚y=60 find the value of tan (x+y)​

Answer 1

Step-by-step explanation:

$\tan(x + y) = \frac{ \tan(x) + \tan(y) }{1 - \tan(x) \tan(y) }$

So put x= 45

and y = 60

$\tan(45 + 60) = \frac{ \tan(45) + \tan(60) }{1 - \tan(45) \tan(60) } \\ \\ = \frac{1 + \sqrt{3} }{(1 - 1 \times \sqrt{3}) } \\ \\ = \frac{1 + \sqrt{3} }{1 - \sqrt{3} } \times ( \frac{1 + \sqrt{3} }{1 + \sqrt{3} } ) \\ \\ = \frac{(1 + \sqrt{3}) ^{2} }{ {1}^{2} - ( \sqrt{3} ) ^{2} } \\ \\ = ( \frac{1 + 3 + 2 \sqrt{3} }{1 - 3} ) \\ \\ = - \frac{4 + 2 \sqrt{3} }{2} \\ \\ = - (2 + \sqrt{3} )$