Question

(2) If cosec =
25., then find the value of coto.
(21
20_​

Answer 1

CORRECT QUESTION:

Q: If cosec θ = 25/7 , then what is the value of cot θ?

ANSWER:

• The value of cot θ = 24/7

STEP-BY-STEP EXPLANATION:

GIVEN

• cosec θ = 25/7

TO FIND

• The value of cot θ.

IDENTITIES USED:

• cosec²θ - 1 = cot²θ

FINDING THE VALUE OF COT θ:

⇒ cosec θ = 25/7

• Squaring both sides,

⇒ cosec²θ = 625/49

• Subtract 1 from both sides,

⇒ cosec²θ - 1 = 625/49 - 1

⇒ cot²θ = 625/49 - 49/49

⇒ cot²θ = (625 - 49)/49

⇒ cot²θ = 576/49

⇒ cot²θ = (24/7)²

• Power of both sides cancelled,

⇒ cot θ = 24/7

IDENTITIES TO REMEMBER:

• sin²θ + cos²θ = 1
• cosec²θ - cot²θ = 1
• sec²θ - tan²θ = 1

Answer 2

$\huge\red{\mid{\underline{\overline{\texttt{Correct \:Question}}}\mid}}$

If cosec Θ = $\frac{25}{7}$units, then find the value of cot Θ.

$\huge\pink{\mid{\fbox{\tt{Answer}}\mid}}$

cot Θ = $\frac{24}{7}$units

$\huge\purple{\mid{\fbox{\tt{Solution}}\mid}}$

$\tt\orange{Given:}$

• Cosec Θ = $\frac{25}{7}$units

$\tt\green{To\:Find:}$

• Cot Θ = ?

$\tt\purple{Formula\:Used:}$

⇒(AC)² = (AB)² + (BC)²

or,

(H)² = (P)² + (B)²

⇒$\rm\: Cosec \: Θ = \frac{h}{p}$units

⇒$\rm \: Cot Θ = \frac{b}{p}$units

where,

h = hypotenuse of the triangle.

b = base of the triangle.

p = perpendicular of the triangle.

$\tt\blue{Calculations:}$

Let's find the sides of the triangle

Cosec Θ = $\frac{h}{p} =$$\frac{25}{7}$ units

By comparing, we get :-

hypotenuse = 25 units

perpendicular = 7 units

Now by Pythagoras theorem we can find out the value of base.

(H)² = (P)² + (B)²

substituting the values,

➙(25)² = (7)² + (B)²

➙625 = 49 + (B)²

➙(B)² = 625 - 49

➙B² = 576

➙B = √576

➙B = 24 units

As we know,

$\rm \: <strong>Cot Θ</strong> = \frac{b}{p}$units

now putting the values,

$\rm \: <strong>Cot Θ</strong> = \frac{24}{7}$units

HENCE, THE VALUE OF $\rm \: Cot Θ \: is \: \frac{24}{7}$units