conditional identities in trigonometry

conditional identities in trigonometry are usually based on A,B, C being angles of a triangle or A + B +C = π

examples

If A + B + C = π , show that cosA + cosB + cos C = 1 + 4 sin(A/2)sin(B/2)sin(C/2)

explanation of If A + B + C = π , show that cosA + cosB + cos C = 1 + 4 sin(A/2)sin(B/2)sin(C/2)

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

explanation





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real and imaginary parts of ln(x+iy)

find the real and imaginary parts of ln(x+iy) or logarithm of a complex number,
first express x+iy in modulus amplitude form
then take log

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basic result of complex number for plus two student

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equation of tangent

find the equation for the tangent to y = x^4 at the point where x=2
first substitute x=2 into the given equation to find y to get the point (x1,y1)
at which the tangent is required.
find dy/dx and evaluate it at (x1,y1) to get the slope,m of the tangent
then use (y-y1) = m(x-x1) to get the equation of the tangent

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to find cot(x ) if you are given that sin(x)=2/3 by drawing a triangle

find cot(x ) if you are given that sin(x)=2/3 and that x is acute.

draw a rt. triangle with one angle as x (not the right angle)



choose the opp. side as 2 and hypotenuse as 3 so that the third side is
sqrt(5) (using pythagoras theorem)

so cot(x) = (sqrt 5) /2


some trigonometry formulae

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