Tan theta = 5/12 find the value of cosec theta

a^2 + b^2 = c^2.

12^2 + 5^2 = c^2,
C = 13.

sin A = 5/13.
csc A = 1/sin A = 13/5.

Draw the triangle. It has sides 5-12-13

so, csc theta = 13/5

To find the value of cosec theta, we can use the reciprocal of sine theta. Since sine is the reciprocal of cosec, we will start by finding the value of sine theta.

We know that tan theta is equal to the ratio of the opposite side to the adjacent side in a right-angled triangle. So, let's assume that the opposite side is 5 units and the adjacent side is 12 units.

Using Pythagoras' theorem, we can find the hypotenuse of the triangle. The hypotenuse squared is equal to the sum of the squares of the other two sides.

Hypotenuse^2 = 5^2 + 12^2
Hypotenuse^2 = 25 + 144
Hypotenuse^2 = 169

Taking the square root of both sides, we get:
Hypotenuse = 13

Now, we can calculate the sine of theta using the opposite side and the hypotenuse:
Sine theta = Opposite side / Hypotenuse
Sine theta = 5 / 13

Finally, we can find the cosec of theta, which is the reciprocal of sine theta:
Cosec theta = 1 / Sine theta = 1 / (5/13) = 13/5

Therefore, the value of cosec theta is 13/5.

To find the value of cosec theta, we need to recall the trigonometric identity that relates cosec and sin:

cosec theta = 1/sin theta

Since we know the value of tan theta, we can use another trigonometric identity that relates tan and sin:

tan theta = sin theta / cos theta

From this equation, we can rearrange to solve for sin theta:

sin theta = tan theta * cos theta

Now, to substitute the given value for tan theta (5/12), we still need to find the value of cos theta. We can use another trigonometric identity, which relates tan and sin:

tan theta = sin theta / cos theta

Rearranging this equation gives us:

cos theta = sin theta / tan theta

Substituting the value of tan theta into this equation, we get:

cos theta = sin theta / (5/12)

Next, we substitute the value of cos theta that we just found into the equation for sin theta:

sin theta = (5/12) * (sin theta / (5/12))

Now we can solve for sin theta:

sin theta = (5/12) * (12/5)
= 1

Finally, we can substitute the values of sin theta into the equation for cosec theta:

cosec theta = 1/sin theta
= 1/1
= 1

Therefore, the value of cosec theta is 1.