sin 60° cos 30° + cos 60° sin 30°

cos 60° cos 30° — sin 60° sin 30°

cos 45° cos 30° + sin 45° sin 30°

2 cos²60° + 3 sin²45° — 3 sin²30° + 2 cos²90°

cot²30° — 2cos²30° — (3/4)sec²45° + (1/4)cosec²30°

(sin²30° + 4 cot²45° — sec²60°)(cosec²45° sec²30°)

Show that:

(i)

Verify each of the following:

(i) sin 60° cos 30° — cos 60° sin 30° = sin 30°

(ii) cos 60° cos 30° + sin 60° sin 30° = cos 30°

(iii) 2 sin 30° cos 30° = sin 60°

(iv) 2 sin 45° cos 45° = sin 90°

If A = 45°, verify that:

(i) sin 2A = 2 sin A cos A

(ii) cos 2A = 2 cos²A —1 = 1— 2 sin²A

If A = 30°, verify that:

(i)

(ii)

(iii)

If A = 60° and B = 30°, verify that:

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

(ii) cos (A + B) = cos A cos B — sin A sin B

If A = 60° and B = 30°, verify that:

(i) sin (A — B) = sin A cos B — cos A sin B

(ii) cos (A — B) = cos A cos B + sin A sin B

(iii)

If A and B are acute angles such that tan , show that A + B = 45°.

Using the formula, , find the value of tan 60°, it being given that

Using the formula,, find the value of cos 30°, it being given that cos 60° = 1/2 .

Using the formula, , find the value of sin 30°, it being given that cos 60° =

In the adjoining figure, ΔABC is a right-angled triangle in which B = 90°, ∠A= 30° and AC = 20 cm. Find (i) BC, (ii) AB.

In the adjoining figure, ΔABC ABC is right-angled at B and ∠A= 30°. If BC = 6 cm, find (i) AB, (ii) AC.

In the adjoining figure, ΔABC is right-angled at B and ∠A= 45°. If AC = 3√2 cm, find (i) BC, (ii) AB.

If sin (A + B) =1 and cos (A - B) = 1, 0° ≤ (A + B) ≤ 90° and A > B then find A and B.

If sin (A - B) = 1/2 and cos (A +B) = 1/2 ,0° < (A + B) < 90° and A > B then find A and B.

If tan (A - B) = 1/√3 and tan (A + B) = √3, 0° < (A + B) < 90° and A > B then find A and B.

If 3x = cosec θ and 3/x = cot θ, find the value of

If sin (A + B) = sin A cos B + cos A sin B , and

cos (A - B) = cos A cos B + sin A sin B, find the values of

(i) sin 75° and (ii) cos 15°.