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Q7(ii):
If $\cot \theta = \frac{7}{8}$, evaluate : (ii) $\cot^2 \theta$

Solution :

Given: The trigonometric ratio $\cot \theta = \frac{7}{8}$.

To Find: The value of $\cot^2 \theta$.

Visual Representation:

A B C Adjacent (7k) Opposite (8k) Hypotenuse

Step 1: Understanding the definition of $\cot \theta$

In a right-angled triangle, for an angle $\theta$, the cotangent ratio is defined as the ratio of the length of the adjacent side to the length of the opposite side:

$\cot \theta = \frac{\text{Adjacent side}}{\text{Opposite side}}$

Step 2: Formulating the expression for $\cot^2 \theta$

The expression $\cot^2 \theta$ is mathematically equivalent to $(\cot \theta)^2$. This notation indicates that the entire value of the cotangent of angle $\theta$ must be raised to the power of 2.

Step 3: Substitution and Calculation

Given that $\cot \theta = \frac{7}{8}$, we substitute this value into the expression:

$\cot^2 \theta = (\cot \theta)^2$

$\cot^2 \theta = \left( \frac{7}{8} \right)^2$

Applying the exponent rule $\left( \frac{a}{b} \right)^n = \frac{a^n}{b^n}$:

$\cot^2 \theta = \frac{7^2}{8^2}$

Calculating the squares of the numerator and the denominator:

$7^2 = 7 \times 7 = 49$

$8^2 = 8 \times 8 = 64$

Therefore:

$\cot^2 \theta = \frac{49}{64}$

Final Answer:

Final Answer: \frac{49}{64}


More Questions from Class 10 Mathematics Introduction to Trigonometry EXERCISE 8.1


CBSE Solutions for Class 10 Mathematics Introduction to Trigonometry


Chapters in CBSE - Class 10 Mathematics


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