Question

If cosa =3/5 find the value of 5coseca-4tana/seca+cota

Answer 1

Given: $cosA=\frac{3}{5}$

To find:

The value of $\frac{5cosecA-4tanA}{secA+cotA}$

Step-by-step explanation:

Here, $cosA=\frac{3}{5}$

Then $sinA=\frac{\sqrt{25-9}}{5}=\frac{\sqrt{16}}{5}=\frac{4}{5}$

Thus $tanA=\frac{sinA}{cosA}=\frac{4}{3}$

$\therefore \frac{5cosecA-4tanA}{secA+cotA}$

$=\dfrac{\frac{5}{sinA}-4tanA}{\frac{1}{cosA}+\frac{1}{tanA}}$

$=\dfrac{\frac{5}{\frac{4}{5}}-4\frac{4}{3}}{\frac{1}{\frac{3}{5}}+\frac{1}{\frac{4}{3}}}$

$=\dfrac{\frac{25}{4}-\frac{16}{3}}{\frac{5}{3}+\frac{3}{4}}$

$=\frac{75-64}{20+9}$

$=\frac{11}{29}$

Answer:

The value of $\frac{5cosecA-4tanA}{secA+cotA}$ is $\frac{11}{29}$.

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