cbse class X exam result for chennai region

cbse class X (class 10) exam result for chennai region has been announced . It is available at http://cbseresults.nic.in/
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if A+B+C = 180° , show that cot A cotB + cotBcotC +cotC cotA=1

if A+B+C = 180° ,
show that

tanA +tanB + tanC = tanAtanBtanC and

cot A cotB + cotBcotC +cotC cotA=1



given A+B+C = 180°

implies A + B = 180°- C

implies tan(A + B) = tan(180°- C)

using trigonometry formulae

tan(A + B) = -tan(C)

therefore

[tanA +tanB] / [1-tanAtanB ] = -tanC

cross multiplying

tanA +tanB = -tanC[1-tanAtanB ]

tanA +tanB = -tanC +tanAtanBtanC

or

tanA +tanB + tanC = tanAtanBtanC

divide each term with tanAtanBtanC we get


cot A cotB + cotBcotC +cotC cotA=1

some other problems
If A+B+C=π,
prove that: sinA+sinB+sinC = cot(A/2).cot(B/2) [sinA+sinB-sinC]

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some useful symbols

≡ ~
± ∓
∤ ◅
∈ ∉
⊆ ⊂ ∪ ∩ ⊥ ô
≈
≅
≠
≤
≥
·
∫ Σ → ∞
Π Δ Φ Ψ Ω Γ ∮ ∇∂ √ ∅ °
α β γ δ ε ζ η θ
ι κ λ μ ν ξ ο π
ρ σ τ υ φ χ ψ ω x²
some interesting symbols for posting into forums.


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confidence interval

confidence interval for population proportion (P) is

( p - (z)sqrt(pq/n) , p + (z)sqrt(pq/n) )

where z is the table value corresponding to the required confidence level, (two tailed)
p the sample proportion , q = 1 - p
n = sample size

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inverse and direct variation

u is said to be directly proportional to v if u = c v for some constant c

u is said to be inversely proportional to v if u = [k / v] for some constant k

In direct variation, u increases as v increases and vice versa.

In inverse variation, u decreases as v increases and vice versa.


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problem of splitting into real and imaginary parts

if u+iv = (x +iy) ^3 , show that (u/x) + (v/y) = 4( x² -y² )

first expand (x +iy) ^3 using binomial expansion or identity and then split into real and imaginary parts then manipulate


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integral of (cos x)^3

integral of (cos x)^3

the (cosx)^3 is split into (cos²x )cosx

the cos²x is written as 1 - sin²x (using trigonometry formulae)

then the substitution t = sinx , dt=cosx dx is used

more explanation is given below


click here for integration formulae


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