Prove that [cot(x)] / [csc(x)] = cos(x)
First lets try to write everything in sines and cosines cot(x) = cos(x) / sin(x) csc(x) = 1 /sin(x) So now we have: [ cos(x) / sin(x) ] / [ 1 /sin(x) ] Since we have a fraction divided by a fraction we can multiply by the reciprocal [ cos(x) / sin(x) ] * [ sin(x) / 1 ] Our sin(x) would cancel out leaving us with [ cos(x) / 1 ] * [ 1 / 1 ] Which would be: cos(x) * 1 which is just cos(x) Which is what we wanted to prove.
The number of ways in which the letters of the word ARTICLE can be arranged taking 3 at a time is?
Here, we are going to use the concept of permutation. The answer regarding to this will be P(7,3). We know P(7,3) means we are going to find the number of ways to choose 3 objects out of total 7 objects available and also such that the arrangement matters. So, the value of P(7,3) = 7! / (7-3)! = 210. Hence, 210 is the required answer.
What is Newton's Third Law of Motion?
Newton's Third Law of Motion states that to every action, there is Equal but Opposite reaction. In real life, it means that if exerts a force on B, B exerts the same quantity of force on A, but the force A experiences is in the opposite direction to what force B experienced. It must be noted that both the objects experience force. So, if you slap on somebody's cheek with your hand, the force towards cheek is an action. The cheek hits back towards the hand at equal force; it's a reaction. The law also holds true for pulling forces like in gravitational forces. The earth pulls on an apple with the same force as the apple pulls on the earth. The effect of force is not so clear because of the masses of earth and apple. The same force produces high acceleration on small apple as compared to a huge earth.