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## NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.1

### Introduction to Trigonometry – Class 10 Maths

#### Practice Question Selected form CBSE Board Papers

- Question 1: If tan A = √2 – 1, show that sin A cos A = √2/4.
- Question 2: In a rectangle ABCD, AB = 20 cm and angle BAC = 60⁰. Find the measure of side BC and diagonals AC and BD. [Answer: BC = 20 √3 cm, AC = 40 cm, BD = 40 cm]
- Question 3: If A is an acute angle and cosec A = √5,
- (i) evaluate cot A – cosec A [Answer: (i) 2 – √5]
- (ii) Verify the identity sin²A + cos²A = 1.

- Question 4: If tan A + cot A = 2, find the value of tan²A + cot²A. [Answer: 2]
- Question 5: In ΔABC, right angled at angle B, AC – BC = 8 cm and AB = 12 cm. Find the value of sec C + 4 cot A. [Answer: 61/5]
- Question 6: If sec A + tan A = p, then find the value of cosec A. [Answer: [p² +1]/[p² – 1]]
- Question 7: If sin A = c/[√(c² + d²] and d > 0, find the value of cos A and tan A. [Answer: cos A = 2/[√(c² + d²)]; tan A = c/d]
- Question 8: In each of the following one of the six trigonometric ratio is given. Find the value of the other trigonometric ratios.
- (i) sin A = 7/25
- (ii) cos A = 9/41
- (iii) tan A = 8/15
- (iv) cosec A = √2
- (v) sec A = 13/12
- (vi) cot A = 20/21

[Answer: (i) cos A = 24/25 , tan A = 7/24, cosec A = 25/7 , sec A = 25/24 , cot A = 24/7

(ii) sin A = 40/41, tan A = 40/9, cosec A = 41/40 , sec A = 41/9 , cot A = 9/40

(iii) sin A = 8/17, cos A = 15/17, cot A = 15/8, cosec A = 17/8, sec A = 17/15

(iv) cos A = 1/√2, tan A = 1, sec A= √2, cot A = 1, sin A = 1/√2

(v) sin A = 5/13, cos A = 12/13, tan A = 5/12, cosec A 13/5, cot A = 12/5

(vi) sin A = 21/29, cos A = 20/29, tan A = 21/20, cosec A = 29/21, sec A = 29/20]