NCERT Class 10 Maths — Chapter 8

Exercise 8.3: Complementary Angles

Use the fact that sin(90°-θ) = cos θ (and similar) to simplify expressions. These identities connect pairs of angles that add up to 90°.

complementary anglessin(90°-θ) = cos θco-function identities
7
NCERT Questions
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Extra Practice Questions

These questions cover the same concepts as Exercise 8.3. Try solving them to build confidence before or after the textbook exercise.

1

In a right-angled triangle ABC, right-angled at B, AB = 8 cm and BC = 15 cm. If BP is the altitude to the hypotenuse AC, then what is the value of sin (∠ABP)?

A.8/17
B.15/17
C.17/8
D.17/15
2

Which of the following statements about trigonometric ratios for an acute angle A is ALWAYS true?

A.sin A > 1
B.sec A < 1
C.tan A can be greater than 1
D.cos A can be 5/3
3

If sin A = 3/5, what is the value of cos A?

A.4/5
B.3/4
C.5/3
D.1
4

Ravi was asked to find cos P for a right-angled triangle PQR, right-angled at Q. He drew the triangle and wrote: cos P = PQ / PR. What mistake, if any, did Ravi make?

A.No mistake, the formula is correct.
B.He should have written cos P = QR / PR.
C.He should have written cos P = PQ / QR.
D.He should have written cos P = QR / PQ.
5

Evaluate: (5 cos² 60° + 4 sec² 30° - tan² 45°) / (sin² 30° + cos² 30°)

A.67/12
B.58/12
C.69/12
D.71/12
6

Ravi states that if tan(A+B) = 1 and tan(A-B) = √3, then A = 60° and B = -15°. Which of the following statements about Ravi's conclusion is correct, assuming A and B are acute angles?

A.Ravi's values for A and B are correct.
B.Ravi made a calculation error; A and B should be 45° and 15° respectively.
C.Ravi made a conceptual error because B cannot be a negative angle if B is acute.
D.Ravi made a conceptual error because A+B = 45° and A-B = 60°, which leads to inconsistent values.
7

A ladder is leaning against a wall, making an angle of 60° with the ground. If the foot of the ladder is 2 meters away from the wall, what is the length of the ladder?

A.2 m
B.4 m
C.2√3 m
D.√3 m
8

Which of the following statements is INCORRECT?

A.sin 0° = 0
B.cos 90° = 0
C.tan 45° = 1
D.sec 0° = 0
9

If A and B are acute angles such that sin A = 1/2 and cos B = 1/2, what is the value of A + B?

A.30°
B.60°
C.90°
D.120°
10

If sec θ + tan θ = p, what is the value of sec θ - tan θ?

A.p
B.1/p
C.p²
D.1 - p
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Common Mistakes to Avoid

  • ✗Forgetting which ratios are complementary pairs (sin↔cos, tan↔cot, sec↔cosec)
  • ✗Not recognising when to apply complementary angle identities

Other Exercises in Chapter 8

Exercise 8.1
Trigonometric Ratios
Exercise 8.2
Trigonometric Ratios of Standard Angles
Exercise 8.3
Complementary Angles
Exercise 8.4
Trigonometric Identities

Frequently Asked Questions

What are complementary angle identities?

sin(90°-θ) = cos θ, cos(90°-θ) = sin θ, tan(90°-θ) = cot θ, and their reverses.

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