Statement 1 : For very small angle `theta`, we may use approximation `sintheta ~~theta~~tantheta.`
and
Statement 2 : For very small angle `theta,` the hypotenuse and the base become approximately of the same length.

Options

A. (1) Statement-1 is True, Statement-2 is True,
Statement-2 is a correct explanation for
Statement-1.
B. (2)Statement-1 is True, Statement-2 is True,
Statemen-2 is not a correct explanation for
Statement-1
C. (3)Statement-1 is True, Statement-2 is False.
D. (4)Statemen-1 is False, Statement-2 is True.

Answer

To analyze the statements provided in the question, we will break down each statement and understand their implications step by step.

### Step 1: Understanding Statement 1
**Statement 1**: For very small angle \( \theta \), we may use the approximation \( \sin \theta \approx \theta \approx \tan \theta \).

- For small angles (in radians), the values of \( \sin \theta \) and \( \tan \theta \) can be approximated by the angle itself. This is derived from the Taylor series expansions of sine and tangent functions.
- As \( \theta \) approaches 0, both \( \sin \theta \) and \( \tan \theta \) approach \( \theta \).

### Step 2: Understanding Statement 2
**Statement 2**: For very small angle \( \theta \), the hypotenuse and the base become approximately of the same length.

- In a right triangle, if we denote the opposite side as \( a \), the base as \( b \), and the hypotenuse as \( c \), we can analyze the relationships.
- As \( \theta \) becomes very small, the height \( a \) (opposite side) becomes very small compared to the base \( b \) (adjacent side) and the hypotenuse \( c \).
- In this case, the base \( b \) and the hypotenuse \( c \) can be considered approximately equal because the angle \( \theta \) is small, leading to a very flat triangle.

### Step 3: Conclusion
- Since both statements are true, we can conclude that Statement 1 is correct, and Statement 2 provides a correct explanation for Statement 1.

### Final Answer
Both statements are true, and Statement 2 is a correct explanation of Statement 1.

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