EXERCISE
1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm.
Determine : (i) sin A, cos A
(ii) sin C, cos C
2. In Fig., find tan P – cot R.
3. If sin A =$3/4$ ,calculate cos A and tan A.
4. Given 15 cot A = 8, find sin A and sec A.
5. Given sec θ = $13/12$, calculate all other trigonometric ratios.
6. If ∠ A and ∠ B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.
7. If cot θ = $7/8$, evaluate : (i) ${(1 + sin θ) (1 − sin θ)}/{(1 + cos θ)(1 − cos θ)}$ , (ii)cot2 θ
8. If 3 cot A = 4, check whether ${1 − tan^2 A}/{1 + tan^2A}$ = $cos^2A – sin^2A$ or not.
9. 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
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.
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 θ = $4/3$ for some angle θ.
Solution