Show that cosh(x+y) = cosh(x)cosh(y) + sinh(x)sinh(y)
RHS: cosh(x)cosh(y) + sinh(x)sinh(y) = 1/4(e^x + e^-x)(e^y + e^-y) + 1/4(e^x - e^-x)(e^y - e^-y) = 1/4(e^x.e^y + e^x.e^-y + e^-x.e^y + e^-x.e^-y + e^x.e^y - e^x.e^-y - e^-x.e^y + e^-x.e^-y) = 1/4(2e^x.e^y + 2e^-x.e^-y) = 1/2(e^x.e^y + e^-x.e^-y) = 1/2(e^(x+y) + e^-(x+y)) = cosh(x+y) [QED]
AH
Related Maths A Level answers
All answers ▸Find the equation of the tangent to the curve y = 3x^2(x+2)^6 at the point (-1,3), in the form y = mx+c
Find the gradient of the curve y=2sinx/x^3 at the point x=
Show that the equation 2sin^2(x) + 3sin(x) = 2cos(2x) + 3 can be written as 6sin^2(x)+3sin(x) - 5 = 0. Hence solve for 0 < x < 360 degrees. Giving your answers to 1.d.p.
Evaluate the integral ∫2x√(x^2 +1) dx