Question

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Answer 1

$\large\tt\underbrace{\red{SOLUTION:-}}$

GIVEN :-

• $\rm{7\:\cot\theta\:=\:24\:}$

$\rm{\implies\:\cot\theta\:=\:\dfrac{24}{7}\:}$

$\checkmark\:\bf{\green{\boxed{\cosec^2\theta\:-\:\cot^2\theta\:=\:1\:}}}$

$\rm{\implies\:\cosec\theta\:=\:\sqrt{(1\:+\:\cot^2\theta)}\:}$

$\rm{\implies\:\cosec\theta\:=\:\sqrt{1\:+\:(\dfrac{24}{7})^2}\:}$

$\rm{\implies\:\cosec\theta\:=\:\sqrt{\dfrac{625}{49}}\:}$

$\rm{\boxed{\implies\:\cosec\theta\:=\:\dfrac{25}{7}\:}}$

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CALCULATION :-

$\rm{\dfrac{1\:-\:\cos\theta}{1\:+\:\cos\theta}\:}$

$\large\rm{=\:\dfrac{\dfrac{1\:-\:\cos\theta}{\sin\theta}}{\dfrac{1\:+\:\cos\theta}{\sin\theta}}\:}$

$\large\rm{=\:{\dfrac{{\dfrac{1}{\sin\theta}}\:-\:{\dfrac{\cos\theta}{\sin\theta}}}{{\dfrac{1}{\sin\theta}}\:+\:{\dfrac{\cos\theta}{\sin\theta}}}}\:}$

$\large\rm{=\:\dfrac{\cosec\theta\:-\:\cot\theta}{\cosec\theta\:+\:\cot\theta}\:}$

$\large\rm{=\:\dfrac{{\dfrac{25}{7}}\:-\:{\dfrac{24}{7}}}{{\dfrac{25}{7}}\:+\:{\dfrac{24}{7}}}\:}$

$\large\rm{=\:\dfrac{\dfrac{1}{7}}{\dfrac{49}{7}}\:}$

$\large\rm{=\:\dfrac{1}{49}\:}$

Answer 2

Answer:

1/49

Step-by-step explanation:

see the attachment for the solution