Exercise 8.1 (Trigonometry)

In ∆ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine :

(i) sin A, cos A

(ii) sin C, cos C

In Fig. 8.13, find tan P - cot R.

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

Given 15 cot A = 8, find sin A and sec A.

Given sec θ = 13/12, calculate all other trigonometric ratios.

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

If cot θ = $\frac{7}{8}$, evaluate 

(i) $\frac{(1+\sin \mathrm{\theta })(1-\sin \mathrm{\theta })}{(1+\cos \mathrm{\theta })(1-\cos \mathrm{\theta })}$,

(ii) cot² θ

If 3 cot A = 4, check whether $\frac{1-{\tan }^2 \mathrm{A}}{1+{\tan }^2 \mathrm{A}}={\cos }^2 A - {\sin }^2 A$ or not

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

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.

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.