Given that t-tan h 2 x- prove the identitiesa sin hx - 2t 1- t 2b cos hx - 1- t 2 1- t 2Hence- or otherwise- solve the equation 2sin hx -cos hx -2tan h 2 x

Given t=tanh12x (a) sinhx=2tanh12x1 tanh^212x #160; #160; #160; #160; #160; #160; #160; #160; #160; = 2t1 t^2 (b) co ...

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Integration Using Substitution

Given that ...

Question

Given that $t \equiv tan \frac{h}{2} x$ , prove the identities
(a) $sin h x = \frac{2 t}{1 - t^{2}}$
(b) $cos h x = \frac{1 + t^{2}}{1 - t^{2}}$
Hence, or otherwise, solve the equation
$2 sin h x - cos h x = 2 tan \frac{h}{2} x$

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