In Δ 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.

If sin calculate Cos A and tan A

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

Given sec calculate all other trigonometric ratios

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

If evaluate:

(i)

(ii)

If 3 cot A = 4, check whetheror not

In triangle ABC, right-angled at B, if find the value of:

(i) Sin A Cos C + Cos A Sin C

(ii) Cos A Cos C – Sin A Sin C

In Δ 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) Secfor 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) for some angle θ

Evaluate the following:

(i)

(ii)

(iii)

(iv)

(v)

Choose the correct option and justify your choice:

Choose the correct option and justify your choice:

Choose the correct option and justify your choice:

Sin 2A = 2 sin A is true when A =

Choose the correct option and justify your choice:

If and find A and B

State whether the following are true or false. Justify your answer

(i) Sin (A + B) = sin A + sin B

(ii) The value of sin θ increases as θ increases

(iii) The value of cos θ increases as θ increases.

(iv) Sin θ = cos θ for all values of θ.

(v) Cot A is not defined for A = 0°

Evaluate:

(i)

(ii)

(iii) Cos 48° – sin 42°

(iv) Cosec 31° – sec 59°

Show that:

(i) tan 48° tan 23° tan 42° tan 67° = 1

(ii) cos 38° Cos 52° – sin 38° sin 52° = 0

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

If tan A = cot B, prove that A + B = 90°

If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A

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

Express sin 67° + Cos 75° in terms of trigonometric ratios of angles between 0° and 45°

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A

Write all the other trigonometric ratios of ∠ A in terms of sec A

Evaluate:

(i)

(ii) Sin 25° Cos 65° + Cos 25° Sin 65°

Choose the correct option. Justify your choice.

Choose the correct option. Justify your choice.

Choose the correct option. Justify your choice.

(Sec A + tan A) (1 – sin A) =

Choose the correct option. Justify your choice.

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

(i)

(ii)

(iii)

(iv)

(v) using the identity

(vi)

(vii)

(viii)

(ix) [Hint: Simplify LHS and RHS separately]

(x)

Draw the graph of 2x – 3y = 4. From the graph, find whether x = -1, y = -2 is a solution or not. (Final)