Solving trig equation
sin ( - 7x) = cos(2-5x) + sin8
Interval - [ ;1]
What I did: 1) sin ( - 7x) = sin cos7x + sin(7x)cos( )
2) cos(2-5x) = cos2cos5x + sin2sin5x
..and 3) sin8 = sin2
But what should I do now, should I multiply by ? Thank you.
Do you mean or
Same for the other terms.
Sorry, it is
Originally Posted by e^(i*pi)
So, your original equation was, if I'm reading it correctly:
Now, considering that and that the 'pi'-es on both sides cancel each other out, the equation turns to:
By squaring both sides, we'll be able to use an identity that'll get rid of the unsightly fraction in the sine:
And after multiplying it by (-1), we convert it from a sum to a product:
Which is equivalent to:
and by equating each factor with zero, you get the solutions:
We find the solution within the interval by including arbitrary values of the integer 'k'. By including k=1, we find the only solution, derived from the first general solution, and that is:
Hope I helped!
That's so much easier. Forget mine :D