please see attached file regarding my problem.
You have two sums where the index of summation is h, these are different h's (that is they are dummy indices of summation).
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CB
p(t)=v(t)*i(t)
p is the electrical power consumed by a consumer.
voltage:v(t)=vh*sinhwt
current:i(t)=ih*sin(hwt+phih)
h is harminic number of main sin wave.that is from 1 to n=50.
to calculate p(t) we must multiply v(t) and i(t)
sentences with v and i of different h are distortion power that are not my requirement.
sentences with v and i of same h must be involved sin2hwt and cos2hwt that are active power and reactive power.
i want to multiply two sigma and gain active and reactive power.
formula in attached file has an error.first sigma must be v(h)*sin(hwt) and second sigma must be i(h)sin(hwt-phih)
sorry for error.i am too busy and confused.
i want simple form of equation not the answer of equation.
after multiplying two sigma we will have two type sentences:$\displaystyle \sum\limits_{h=1}^n{\sin(h*w*t)*ih*vh*sin(h*w*t-phi)}$
in ih and vh, h is index.
the other type is not my aim.
in this sentence how can i change sin(h*w*t)*sin(h*w*t-phi) to sin(2*h*w*t) and cos(2*h*w*t)?