Assertion (A): If two acute angles add up to 90°, their sines are equal. Reason (R): The sum of angles

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Q.
Assertion (A): If two acute angles add up to $90 °$ , their sines are equal.

Reason (R): The sum of angles in a right triangle is $180 °$ , and one of the angles is $90 °$ .

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans.
(4)

The assertion is false because the sine of angles that add up to $90 °$ are equal to its cosine and vice-versa. The reason is true, as it describes the fundamental property of angle sums in a right triangle.

Solution

Q.
Assertion (A): If two acute angles add up to $90 °$ , their sines are equal.

Reason (R): The sum of angles in a right triangle is $180 °$ , and one of the angles is $90 °$ .

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans.
(4)

The assertion is false because the sine of angles that add up to $90 °$ are equal to its cosine and vice-versa. The reason is true, as it describes the fundamental property of angle sums in a right triangle.

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Solution

Q. Assertion (A): If two acute angles add up to 90°, their sines are equal. Reason (R): The sum of angles in a right triangle is 180°, and one of the angles is 90°.

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans. (4) The assertion is false because the sine of angles that add up to 90° are equal to its cosine and vice-versa. The reason is true, as it describes the fundamental property of angle sums in a right triangle.

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Q.
Assertion (A): If two acute angles add up to $90 °$ , their sines are equal.

Reason (R): The sum of angles in a right triangle is $180 °$ , and one of the angles is $90 °$ .

Ans.
(4)

The assertion is false because the sine of angles that add up to $90 °$ are equal to its cosine and vice-versa. The reason is true, as it describes the fundamental property of angle sums in a right triangle.