Assertion (A): For triangle ABC, sec $\Big(\dfrac{A+B}{2}\Big) = \text{cosec C}$.

Reason (R): sec (90° - θ) = cosec θ.

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): If ∠A = 30°, the value of tan² 2A - sec² 2A is 1.

Reason (R): tan² 2A - sec² 2A = tan² 60° - sec² 60°
= $(\sqrt3)^2 - (2)^2 = -1$

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): Area of given rhombus = 10 cm x 10 cm = 100 cm²

Reason (R):

⇒ OA = $5\sqrt{3}$ cm
⇒ AC = 2 x $5\sqrt{3}$ cm = $10\sqrt{3}$ cm
⇒ OB = 5 cm
⇒ BD = 2 x 5 cm = 10 cm

Area of rhombus ABCD = AC x BD = 10 x 10 cm² = 100 cm²

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): CD = 3 x AB = 3 x 10 m = 30 m

Reason (R): In △ABC, tan30° = $\dfrac{10\text{m}}{\text{BC}}$
⇒ BC = 10 $\sqrt{3}$ m
tan 30° = $\dfrac{10\sqrt{3}\text{m}}{\text{CD}}$
⇒ CD = 30 m

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.