Question

if cot theta =24/7 find sec theta and cosec theta​

Answer 1

if cot theta =24/7 find sec theta and cosec theta​

Answer 2

Answer:

The answer is cosec θ = $\frac{25}{7}$ and sec θ = $\frac{25}{24}$

Step-by-step explanation:

We have to use the formulas of trigonometry to solve the above-given problem. The formulas that need to be considered are as follows:

cot θ = 1 / tan θ

Therefore we have been given,

cot θ = 24 / 7

Hence tan θ = 7/ 24

As we have tanθ = perpendicular/base

Therefore the base (b) and perpendicular (p) respectively of the given right angled triangle are 7 and 24 respectively.

Therefore using Pythagoras theorem the hypotenuse (h)will be

$b^{2} + p^{2} = h^{2}$

⇒$7^{2}+ 24^{2} =h^{2}$

⇒ 49 + 576 = $h^{2}$

⇒ 625 = $h^{2}$

⇒ $h^{2} = 25^{2}$

⇒ h = 25

Now we have hypotenuse to be 25.

Therefore cosθ = base / hypotenuse = $\frac{24}{25}$

sin θ = perpendicular / hypotenuse = $\frac{7}{25}$

As we know that sec θ = 1 / cos θ

∴ sec θ = $\frac{25}{24}$

cosec θ = 1 / sin θ

∴ cosec θ = $\frac{25}{7}$

Hence we have sec θ = $\frac{25}{24}$ and cosec θ = $\frac{25}{7}$.