## 1. If sin θ = 3/5 and θ is an acute angle, then cos θ is:

### Answer:

### Explanation:

Using the Pythagorean identity, cos² θ = 1 – sin² θ. So, cos θ = √(1 – (3/5)²) = 4/5.

## 2. The value of tan 45° is:

### Answer:

### Explanation:

tan 45° = sin 45°/cos 45° = 1/√2 ÷ 1/√2 = 1.

## 3. If cos A = 1/√2, then the value of A is:

### Answer:

### Explanation:

cos 45° = 1/√2.

## 4. The reciprocal of cosec θ is:

### Answer:

### Explanation:

cosec θ is the reciprocal of sin θ.

## 5. The value of sin²θ + cos²θ is always:

### Answer:

### Explanation:

This is the fundamental Pythagorean identity in trigonometry.

## 6. The trigonometric ratio which is independent of θ in the first quadrant is:

### Answer:

### Explanation:

In the first quadrant, all trigonometric ratios are positive.

## 7. If tan θ = √3, then the value of sin θ is:

### Answer:

### Explanation:

For tan θ = √3, θ = 60°. So, sin 60° = √3/2.

## 8. The value of cos 90° is:

### Answer:

### Explanation:

cos 90° = 0 as the cosine function represents the x-coordinate on the unit circle.

## 9. If sin θ = x and cos θ = y, then (x² + y²) equals:

### Answer:

### Explanation:

Given, sin²θ + cos²θ = 1.

## 10. The general solution for the equation sin x = 0 is:

### Answer:

### Explanation:

sin function is zero at integral multiples of π.

## 11. If sec A = 13/12, then tan A is:

### Answer:

### Explanation:

tan A = √(sec²A – 1) = 5/13.

## 12. For which of the following angles, sin and cos have the same value?

### Answer:

### Explanation:

sin 45° = cos 45° = 1/√2.

## 13. The period of the function sin(x) is:

### Answer:

### Explanation:

The function sin(x) repeats after an interval of 2π.

## 14. Which trigonometric ratio is always positive?

### Answer:

### Explanation:

sec is positive in the first and fourth quadrants.

## 15. The maximum value of sin x is:

### Answer:

### Explanation:

The sine function oscillates between -1 and 1.

## 16. The value of tan(A + B) in terms of tan A and tan B is:

### Answer:

### Explanation:

This is the compound angle formula for tan(A + B).

## 17. If sin θ = a/c, then csc θ is:

### Answer:

### Explanation:

csc θ is the reciprocal of sin θ.

## 18. The range of the sine function is:

### Answer:

### Explanation:

The sine function varies between -1 and 1.

## 19. If cos θ = 0, then θ is:

### Answer:

### Explanation:

cos 90° = 0.

## 20. The trigonometric ratio that represents the length of the side opposite to the angle to the hypotenuse is:

### Answer:

### Explanation:

Sin θ = Opposite side/Hypotenuse.