Yay A-Level maths. -.-
Okay got the following hyperbolic trig equation to solve:
Solve the equation 2tanh^2(x) - sech(x) = 1, giving your answer(s) in logarithmic form.
I started off by multiplying through by cosh^2(x) to get:
2sinh^2(x) - cosh(x) = cosh^2(x)
Then
2(1 - cosh^2(x)) - cosh(x) = cosh^2(x)
2 - 2cosh^2(x) - cosh(x) = cosh^2(x)
3cosh^2(x) + cosh(x) = 2
Then using identities cosh(x) = 0.5(e^x + e^-x)
I got it down to
something which worked out completely wrong =/
Maybe I should have converted to the exponential form right at the start,
any pointers?
thanks.
Okay got the following hyperbolic trig equation to solve:
Solve the equation 2tanh^2(x) - sech(x) = 1, giving your answer(s) in logarithmic form.
I started off by multiplying through by cosh^2(x) to get:
2sinh^2(x) - cosh(x) = cosh^2(x)
Then
2(1 - cosh^2(x)) - cosh(x) = cosh^2(x)
2 - 2cosh^2(x) - cosh(x) = cosh^2(x)
3cosh^2(x) + cosh(x) = 2
Then using identities cosh(x) = 0.5(e^x + e^-x)
I got it down to
something which worked out completely wrong =/
Maybe I should have converted to the exponential form right at the start,
any pointers?
thanks.
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