Question

If cosee o=s
o =s then find the value
3
ol los ottan o

Answer 1

Given:-

$\implies \: \cosec \theta = \frac{5}{3}$

Find:-

$\implies \: \cos\theta + \tan \theta = {?}^{}$

SOLUTION:-

we know that

$\implies \red{\cosec \theta = \frac{h}{p} }$

$\implies \: \cosec \theta = \frac{5}{3}$

h=5 and p=3

we know that Pythagoras theorem

$\implies \pink{h = \sqrt{p {}^{2} + b {}^{2} } } \\ \\ \implies \pink{b = \sqrt{h {}^{2} - p {}^{2} } }$

put value

$\implies \: b = \sqrt{5 {}^{2} - 3 {}^{2} } \\ \\ \implies \: b = \sqrt{25 - 9} \\ \\ \implies \: b = \sqrt{16} \\ \\ \implies \: b = 4$

we know that

$\implies \: \cos \theta = \frac{b}{h} = \frac{4}{5}$

and

$\implies \: \tan \theta = \frac{p}{b} = \frac{3}{4}$

$\implies \: \cos \theta + \tan \theta \\ \\ \implies \: \frac{4}{5} + \frac{3}{4} \\ \\ \implies \: \frac{16 + 15}{20} \\ \\ \implies \: \frac{31}{20}$

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I hope it helps you