# MATH – TEST 2 – CHAPTER 8 & 9 Trigonometry

**NEUTRON CLASSES**

**CLASS – X**

**MATH – TEST 2 – CHAPTER 8 & 9**

**Q. 1. **In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.

**Q. 2. **In ∆ OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm. Determine the values of sin Q and cos Q.

**Q. 3. **In triangle ABC, right-angled at B, if tan A = 1/√3 find the value of:

(i) sin A cos C + cos A sin C

(ii) cos A cos C – sin A sin C

**Q. 4.** If tan (A + B) = √3 and tan (A – B) = 1/√3 ; 0° < A + B ≤ 90°; A > B, find A and B.

**Q. 5. **If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.

**Q. 6. **Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

**Q. 7. **(sin A + cosec A)^{2} + (cos A + sec A)^{2 }= 7 + tan^{2} A + cot^{2} A.

**Q. 8. **(cosec A – sin A)(sec A – cos A) = 1 / tan A + cot A.

**Q. 9. **The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.

**Q. 10. **The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings.