Use the exponential definition of sinh(x) and cosh(x) to show cosh (X) = cosh(2x)+2 b) Solve the equation 6 cosh(4x) + 30 sinh(4x) = 15, giving your answer in terms of a natural logarithm
Question 2 (4 marks total)
Without using a calculator, solve the following system of equations for x E and y E , given: a) log2(m2 — 6m) = 2 log2(1 — m) — 2 (1 marks) b) 24Y+1 — 3Y = 0 (1 marks)
c) 4Y I=32 log3(x— y)+ log3(x+ y) = I
(2 marks)
Hint: Solving these problems will require careful application of exponent and logarithm identities. Question 3 (3 marks total) Prove the following identities a) tan( x + 1i) = — cot x b) cos (x—y) = tan x + cot y cos x cos y C) cosx(1—cos(2.0) = sin xsin (2x)
Hint: Do not attempt to substitute values and then solve. You must arrive at a solution algebraically through application of trigonometric identities.
Question 4 (4 marks total)
Solve the following trigonometric equations, for 0