Question

If cot theta =7/24 then find the value of sin theta *sec theta /1+ cosec theta *tan theta

Answer 1

Answer:

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Answer 2

The value is 0.75

Step-by-step explanation:

$Cot \theta = \frac{Base}{Perpendicular}$

$Cot \theta = \frac{7}{24}$

On comparing

Base = 7

Perpendicular = 24

$Hypotenuse^2=Perpendicular^2+Base^2 \\Hypotenuse= \sqrt{24^2+7^2}$

Hypotenuse =25

$Sin \theta = \frac{Perpendicular}{Hypotenuse} =\frac{24}{25} \\Sec \theta = \frac{Hypotenuse}{Base}=\frac{25}{7} \\Cosec \theta = \frac{1}{sin\theta}=\frac{25}{24} \\Tan \theta = \frac{1}{cot\theta}=\frac{24}{7}$

So,$\frac{Sin \theta \times sec \theta }{1+cosec \theta \times tan \theta}=\frac{\frac{24}{25} \times \frac{25}{7}}{1+(\frac{25}{24} \times \frac{24}{7})}=0.75$

Hence The value is 0.75

#Learn more:

If tan theta =1, then find the values of sin theta + cos theta/ sec theta + cosec theta

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