Question

If cos θ = 3/5, show that (sinθ - cotθ)/ 2tanθ = 3/160

Answer 1

Answer :

Given that, cosθ = 3/5

So, sinθ

= {√(5² - 3²)}/5

= {√(25 - 9)}/5

= {√16}/5

= 4/5

∴ tanθ = 4/3 and cotθ = 3/4

Now, (sinθ - cotθ) / (2 tanθ)

= (4/5 - 3/4) / (2 * 4/3)

= (16 - 15)/20 * 8/3

= 1/20 * 8/3

= 3/160

Hence, proved.

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Answer 2

SOLUTION:-

Given:

If cos theta= 3/5.

To find:

Show that (sin theta -cot theta)/2 tan theta) = 3/160

Explanation:

$cos \theta = \frac{Base}{Hypotenuse} = \frac{3}{5}$

Using the Pythagoras Theorem:

H² = B² + P²

=) 5² = 3² + P²

=) 25 = 9 +P²

=) P² = 25 -9

=) P² = 16

=) P= √16

=) P= 4

Now,

$\frac{sin \theta - cos \theta}{2tan \theta} \\ \\ = > \frac{ \frac{P}{H} - \frac{B}{P} }{2 \times \frac{P}{B} } \\ \\ = > \frac{ \frac{4}{5} - \frac{3}{4} }{2 \times \frac{4}{3} } \\ \\ = > \frac{ \frac{16 - 15}{20} }{ \frac{8}{3} } \\ \\ = > \frac{ \frac{1}{20} }{ \frac{8}{3} } \\ \\ = > \frac{1}{20} \times \frac{3}{8} \\ \\ = > \frac{3}{160} = \frac{3}{160}$

Thank you.