Question

19. Given 5 cos A - 12 sin A = 0, find the value of
sin A + cos A/

2 cos A - sin A
(ICSE 1995)​

Answer 1

Step-by-step explanation:

$5 \cos( \alpha ) - 12 \sin( \alpha ) = 0 \\ 5 \cos( \alpha ) = 12 \sin( \alpha )$

Now,

$\frac{ \sin( \alpha ) + \cos( \alpha ) }{2 \cos( \alpha ) - \sin( \alpha ) } \\ = \frac{ \sin( \alpha ) + \cos( \alpha ) }{2 \cos( \alpha ) - \sin( \alpha ) } \times \frac{5}{5}$

$= \frac{5 \sin( \alpha ) + 5\cos( \alpha ) }{10 \cos( \alpha ) - 5\sin( \alpha ) } = \frac{13 \sin( \alpha ) }{19 \sin( \alpha ) } \\ = \frac{13}{19}$

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