NCERT Class 10 Maths — Chapter 8

Exercise 8.4: Trigonometric Identities

Prove trigonometric identities using the three fundamental relationships. This exercise tests algebraic manipulation with trig functions.

sin²θ + cos²θ = 1sec²θ - tan²θ = 1proving identities

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Extra Practice Questions

These questions cover the same concepts as Exercise 8.4. Try solving them to build confidence before or after the textbook exercise.

In a right-angled triangle ABC, right-angled at B, if AB = 8 cm and BC = 6 cm, what is the value of tan A?

A.3/4

B.4/3

C.3/5

D.4/5

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.

A student simplified the expression (sec²A - 1)cot A as follows: Step 1: tan²A × cot A (using 1 + tan²A = sec²A) Step 2: tan²A × (1/tan A) Step 3: tan A Step 4: He concluded the expression is equal to tan A. Which step contains an error in reasoning or calculation?

A.Step 1

B.Step 2

C.Step 3

D.No error

If sin θ = 12/13, what is the value of cosec θ?

A.13/12

B.5/12

C.12/5

D.1/13

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

A.p

B.1/p

C.p²

D.1/p²

If tan A = n tan B and sin A = m sin B, then which of the following expresses cos²A?

A.(m²-1) / (n²-1)

B.(n²-1) / (m²-1)

C.(n²-m²) / (n²-1)

D.(m²-n²) / (m²-1)

Which of the following statements is NOT always true for an acute angle A (0° < A < 90°)?

A.sin A < 1

B.sec A ≥ 1

C.tan A < 0

D.cosec A > 1

Simplify: (1 - sin²A) / (1 - cos²A)

A.tan²A

B.cot²A

C.sec²A

D.cosec²A

Evaluate: (sin 60° × cos 30° + sin 30° × cos 60°)

A.0

B.1/2

C.1

D.√3/2

Ria solved the equation sin²A - 1 = 0 for an acute angle A. She concluded that A = 90°. Which of the following statements about her conclusion is most accurate?

A.A) Her conclusion is always correct.

B.B) Her conclusion is correct only if A is acute.

C.C) Her conclusion is correct, but only if sin A is positive.

D.D) Her conclusion is incomplete, as sin²A = 1 implies sin A = ±1.

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