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bayley86 · Jan 7, 2010, 02:33 PM

use trigonometric and hyperbolic identities to solve and simplify the following:

4sin^2 theta +5cos theta =5
3tan^2 theta+5=7sec theta
prove that cosh^2x-sinh^2x=1
prove that sinh2x=2sinhxcoshx

any help with this would be much appreciated

thanks

Andy

galactus · Jan 7, 2010, 02:40 PM

prove that cosh^2x-sinh^2x=1

They can be expressed in terms of e. This stuff should be in your calc book. Just use them.

$cosh(x)=\frac{e^{x}+e^{-x}}{2}$

$sinh(x)=\frac{e^{x}-e^{-x}}{2}$

Now, apply these identites and do the algebra. You should get 1.

galactus · Jan 7, 2010, 02:50 PM

4sin^2 theta +5cos theta =5

Let's use an identity and try a substitution, then turn it into a quadratic.

$4sin^{2}(t)+5cos(t)=5$

$4(1-cos^{2}(t))+5cos(t)=5$

$4-4cos^{2}(t)+5cos(t)=5$

$-4cos^{2}(t)+5cos(t)-1=0$

Now, let $u=cos(t)$

$-4u^{2}+5u-1=0$

Solve the quadratic and resub.

Unknown008 · Jan 7, 2010, 09:15 PM

Please, do not double post your questions.

https://www.askmehelpdesk.com/math-s...es-432694.html