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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
PROOF OF VARIOUS LIMIT PROPERTIES In this section we are going to prove several of the fundamental facts and properties about limits which we saw previously. Before proceeding
Parametric objective-function problems
If the p th term of an AP is q and the q th term is p. P.T its n th term is (p+q-n). Ans: APQ a p = q a q = p a n = ? a + (p-1) d = q a + (q-1) d = p
2x + 3x
A train goin from delhi to jaipur stops at 7 intermediate stations. 5 persons enter the train during the journey with 5 difefrent tickets of same class . How mant different set of
Relative Frequency This type of probability requires us to make some qualifications. We define probability of event A, occurring as the proportion of times A occurs, if we re
shortricks of compound interest
Using the example provided below, if the measure ∠AEB = 5x + 40 and ∠BEC = x + 20, determine m∠DEC. a. 40° b. 25° c. 140° d. 65° c. The addition of the measurem
Let a and b be fixed real numbers such that a The open interval (a, b): We define an open interval (a, b) with end points a and b as a set of all r
NATURAL NUMBERS The numbers 1, 2, 3, 4.... Are called as natural numbers, their set is shown by N. Hence N = {1, 2, 3, 4, 5....} WHOLE NUMBERS The numbers 0, 1, 2, 3, 4
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