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sin(2x+x)=sin2x.cosx+cos2x.sinx =2sinxcosx.cosx+(-2sin^2x)sinx =2sinxcos^2+sinx-2sin^3x =sinx(2cos^2x+1)-2sin^3x=sinx(2-2sin^2x+1)-2sin^3x =2sinx-2sin^3x+sinx-2sin^3x = 3sinx-4sin^3x
The Shape of a Graph, Part II : In previous we saw how we could use the first derivative of a function to obtain some information regarding the graph of a function. In this secti
Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively. (Ans: 17) Ans: The required number is the HCF of the n
prove that J[i] is an euclidean ring
Here we look at only the rules without going into their proofs. They are: a 0. If a If a If a
1. Find the number of zeroes of the polynomial y = f(x) whose graph is given in figure. 2 Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0) and (7,-6).
a) How many equivalence relations on {a, b, c, d, e, f} have b) How many arrangements are there of c) How many triangles are resolute by the vertices of a regular polygon w
Without solving, find out the Wronskian of two solutions to the subsequent differential equation. t 4 y'' - 2t 3 y' - t 8 y = 0 Solution : First thing that we want to d
in 2000,nearly 18% of cars in north America were sliver. what percent of the cars sold were not sliver?
Logarithm Functions : Now let's briefly get the derivatives for logarithms. In this case we will have to start with the following fact regarding functions that are inverses of ea
The Central Limit Theorem The theories was introduced by De Moivre and according to it; if we choose a large number of simple random samples, says from any population and find
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