Question

-1 12. Simplify tan^-1(a cosx-b sinx/ b cosx +a sinx -) , if a/btanx >- 1​

Answer 1

Step-by-step explanation:

We have,

$\tan^{ - 1} \bigg( \frac{a \cos(x) - b \sin(x) }{b \cos(x) + a \sin(x) } \bigg)$

$= \tan^{ - 1} \bigg( \frac{\frac{a \cos(x) - b \sin(x)}{b \cos(x) } }{ \frac{b \cos(x) + a \sin(x)}{b \cos(x) } } \bigg)$

$= \tan^{ - 1} \bigg( \frac{ \frac{a}{b} - \tan(x) }{1 + \frac{a}{b} \tan(x) } \bigg)$

$= \tan^{ - 1} \bigg( \frac{a}{b} \bigg) - \tan^{ - 1} ( \tan(x) )$

$= \tan^{ - 1} \bigg( \frac{a}{b} \bigg) - x$