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∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + cDetailed derivation of∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx
= ∫(cosec2x - cosecxcotx)/(cosecx - cotx) dx
= log[cosecx - cotx] = log[(1-cosx)/sinx]
= log[2sin2(x/2)/2sin(x/2)cos(x/2)]
= log[tan(x/2)]
We're here going to take a brief detour and notice solutions to non-constant coefficient, second order differential equations of the form. p (t) y′′ + q (t ) y′ + r (t ) y = 0
A long distance calls costs x cents for the first minute and y cents for every additional minute. How much would a 5-minute call cost? The cost of the call is x cents plus y ti
OTHER WAYS TO AID LEARNING : Here we shall pay particular attention to the need for repetition, learning from other children, and utilising errors for learning.
Q) In a lottery ,a person chooses six different natural numbers at random 1to 20,and if there six numbers match with the six numbers already fixed by the lottery committee ,he win
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How to construct a histogram into an ogive
Example: Write down the equation of the line which passes through the two points (-2, 4) and (3, -5). Solution At first glance it might not appear which we'll be capable to
Decimal representations of some basic angles: As a last quick topic let's note that it will, on occasion, be useful to remember the decimal representations of some basic angles. S
Write the next two terms √12, √27, √48, √75................... Ans: next two terms √108 , √147 AP is 2 √3 , 3 √3 , 4 √3 , 5 √3 , 6 √3 , 7 √3 ......
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