IIT JEE , AIEEE Forum - Articles Category , Community shelf - For all JEE and AIEEE aspirants-Trigonometry and Properties of triangle-Revisited

annihilator

Here are some formulae tht u dont see often

tan(A+B+C)= tanA+tanB+tanC-tanAtanBtanC
      1-tanAtanB-tanBtanC-tanAtanC

cosAcos2Acos4A.....n terms=sin(2ⁿA) / 2ⁿ.sinA (divide and multiply by sinA)

sinA+sin(A+B)+sin(A+2B).....to n terms = sin nB/2 x sin[A+(n-1)B/2]
                                                              sinB/2

cosA+cos(A+B)+cos(A+2B)....n terms = sin nB/2 x cos[A+(n-1)B/2]
                                                            sinB/2

sinA+sin2A+sin3A......n terms= sin nA/2 x sin[(n+1)A/2]
                                                  sin A/2

cosA+cos2A+cos3A......n terms= sin nA/2 x cos[(n+1)A/2]
                                                  sin A/2

If A+B+C=

thn :

sin2A +sin2B+sin2C=4sinAsinBsinC

1+

cos2A= - 4cosAcosBcosC

sinA=4cosA/2cosB/2cosC/2

cosA=1+4sinA/2sinB/2sinC/2

tanA=

tanA

cotBcotC=1

cotA/2=

cotA/2

tanA/2tanB/2=1

a/sinA=b/sinB=c/sinC (sine law)
a²=b² + c² -2 b.c cosA (cosine law)
a=b.cosC+c.cosB (projection formula)
tan B-C = b-c x cotA/2
2 b+c
sinA/2=

{(s-b)(s-c)/bc}
cosA/2=

s(s-a)/bc

=

s(s-a)(s-b)(s-c)=abc/4R
r=4R

sinA/2
r1=

/(s-a)
r2=

/(s-b)
r3=

/(s-c)

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