### Exercise 8.1

**Question 1. In AABC, right-angled at B, AB= 24 cm, BC= 7 cm. Determine :(i) sin A, cos A (ii) sin C, cos C**

**Question 2. In given figure find tan P – cot R :**

**Question 3. If sin A = 3/4 calculate cos A and tan A.**

**Question 4. Given 15cotA=8, find sin A and sec A.**

**Question 5. Given sec0 = 13/12, calculate all other trigonometric ratios.**

**Question 6. If LA and LB are acute angles such that cosA = cos B, then show that LA = LB.**

**Note :** Side opposite to any acute angle 0 in right triangle is always perpendicular

**Question 7. If cot0 = 7/8 evaluate :**

**Question 8. If 3cotA = 4, check whether**

**Question 9. In triangle ABC, right-angled at B, if tan A= 1/root3, find the value of:**

**Question 10. In PQR, right-angled at Q, PR + QR= 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.**

**Question 11. State whether the following are true or false. Justify your answer.(I) The value of tan A is always less than 1.(ii) sec A= 12/5 for some value of angle A.(iii) cos A is the abbreviation used for the cosecant of angle A.(iv) cot A is the product of cot and A.(v) sin 0 = 3 for some angle 0.**

### Exercise 8.2

**Question 1. Evaluate the following:**

**Question 2. Choose the correct option and justify your choice:**

**Note :** A fraction having zero in its denominator is undefined.

**Question 3. If tan(A+B)= root 3 and tan(A-B)= 1/root3 ;0° < A+B < 90,find A and B.**

**Question 4. State whether the following are true or false. Justify your answer.(i) sin (A+ B) = sin A+ sin B.(ii) The value of sin 0 increases as 0 increases.(iii) The value of cos 0 increases as 0 increases.(iv) sin 0 = cos 0 for all values of 0.(v) cot A is not defined for A= 0°.**

Exercise 8.3

**Question 1. Evaluate**

**Question 2. Show that**

**Question 3. If tan2A =cot (A-18°), where 2A is an acute angle, find the value of A.**

**Question 4. If tan A= cot B, prove that A + B = 90°.**

**Question 5. If sec4A=cosec(A-20°), where 4A is an acute angle, find the value of A.**

**Question 6. If A, B, and C are interior angles of a triangle ABC, then show that**

**Question 7. Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0°and45°.**

### Exercise 8.4

**Question 1. Express the trigonometric ratios sin A, sec A, and tan A in terms of cot A.**

**Question 2. Write all the other trigonometric ratios of LA in terms of sec A.**

**Question 3. Evaluate :**

**Question 4. Choose the correct option. Justify your choice.**

**Note:** Writing the expression in terms of sin 0 and cos 0 makes it easier to solve.

**Question 5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.**

**Hint :** Writing the expression in terms of sin 0 and cos 0

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