# 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 + tan2 A + cot2 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.

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