1.

If 5 tanθ = 4, then the value of \(\left( {\frac{{5\sin \theta - 3\cos \theta }}{{5\sin \theta + 3\cos \theta }}} \right)\) is1). 1/72). 2/73). 5/74). 2/5

Answer»

Given, 5tanθ = 4

⇒tanθ = 4/5

We have to find the value of $(\LEFT( {\FRAC{{5\sin \theta - 3\cos \theta }}{{5\sin \theta + 3\cos \theta }}} \right))$

$(= \;\left( {\frac{{5\sin \theta - 3\cos \theta }}{{5\sin \theta + 3\cos \theta }}} \right))$

$(=\left( {\frac{{cos\theta (5\frac{{\sin \theta }}{{cos\theta }} - 3)}}{{cos\theta (5\frac{{\sin \theta }}{{cos\theta }} + 3)}}} \right))$ (taking cosθ COMMON from numerator and DENOMINATOR)

$(= \left( {\frac{{5tan\theta - 3}}{{5tan\theta + 3}}} \right))$

$(= \left( {\frac{{5 \times \frac{4}{5} - 3}}{{5 \times \frac{4}{5} + 3}}} \right))$

$(= \frac{{4 - 3}}{{4 + 3}})$

= 1/7


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