What is the simplified value of $\left(\frac{1}{cosecA + cotA}\right)^{2}$ ?1). sec A tan A2). $\frac{(1-cos A)}{(1 cos A)}$3). $\frac{(1-cosec A)}{(1 cosec A)}$4). sin A
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1. A car moving in the morning fog passes a man walking at 4km/h. in the same direction. The man can see the car for 3 minutes and visibility is upto a distance of 130m. The speed of the car is
2. If A is an acute angle and cot A + cosec A = 3, then the value of sin A is
3. If $2sin\left(\frac{\pi x}{2}\right)$ = $x^{2} +\frac{1}{x^{2}}$ , then the value of $\left(x- \frac{1}{x}\right)$ is
4. From two points on the ground lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary toeach other. If the distance of the two points from the foot of the pillar are 9 metres and 16 metres and the two points lie on the same side of the pillar, then the height of the pillar is
5. What is the simplified value of (cosec A + sin A)(cosec A - sin A)?
6. If x =$ a(sin\theta + cos\theta )$, y = $b(sin\theta - cos\theta)$ then the value of $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$ is
7. At a point on a horizontal line through the base of a monument the angle of elevation of the top of the monument is found to be such that its tangent is $\frac{1}{5}$ . On walking 138 metres towards the monument the secant of the angle of elevation is found to be $\frac{\sqrt{193}}{12}$.The height of the monument ( in metre)is
8. What is the value of cosec A sec A cot A - sec A cosec A tan A?
9. A rectangular swimming pool of length 20 m and breadth 10 m has a uniformly sloping floor. It is 1 m in depth on one end of its length and 3 m at the other. How much water is needed to completely fill this pool? (Take π = $\frac{22}{7}$)
10. A man 6 ft tall casts a shadow 4 ft long, at the same time when a flag pole casta a shadow 50 ft long. The height of the flag pole is
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