Question

In a right angle triangle ABC, right angle is at B, if tan A= 73 then find the value of
(i) sin A cos C+ cos A sin C
(ii) cos A cos C-sin A sin C

Answer 1

Step-by-step explanation:

$given \: that \: \\ tan \: a = \frac{ \sqrt{3} }{1} \\ ac = \sqrt{( {3})^{2} + {1}^{2} } \\ = \sqrt{3 + 1 } \\ = \sqrt{4} \\ = 2 \\ now \: \\ 1) \: sin \: a \: cos \: c + cos \: a \: sin \: c \\ = \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} + \frac{1}{2} \times \frac{1}{2} \\ = \frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1 \\ and \: \\ cos \: a \: cos \: c \: - sin \: a \: sin \: c \\ = \frac{1}{2} \times \frac{ \sqrt{3} }{2} - \frac{1}{2} \times \frac{ \sqrt{3} }{2} \\ = \frac{ \sqrt{3} }{2} - \frac{ \sqrt{3} }{2} \\ = 0$