Re: How to simplify "sin(x)^2 + cos(x)^2" to 1 in calc?

[Michael Heerdegen]

Vladimir Nikishkin <lockywolf@gmail.com> writes:

> Hello, everyone.
>
> Please, refer me to a correct mailing list if this one is not
> appropriate,

This one is good.

> I am trying to make calc apply the most basic trigonometric identity,
> and simplify the algebraic formula "sin(x)^2 + cos(x)^2" to 1.
>
> I tried  'a v', 'a "', '=', 'j D', 'j M', but seemingly, all in vain,
> even though "sin(x)^2 + cos(x)^2 = 1" seems to be one of the safest
> substitutions in algebra. (Not sure about 'x having a quaternion value,
> or working in some arithmetic mod p.)
>
> What am I doing wrong?

Nothing, I guess.  It's indeed surprising that Calc fails to perform
this simplification automatically.

This identity is discussed in several places in the Calc manual.  With
the extended algebraic simplification mode enabled, Calc even simplifies
sqrt(1 - sin(x)^2) to cos(x).  But not 1 - sin(x)^2 to cos(x)^2 or
sin(x)^2+cos(x)^2 to 1.

Seems to be a known limitation though: the chapters about rewrite rules
talk about how to apply the Pythagorean trigonometric identity manually.
It seems you have to force the application in most situations.

Calc's automatic rewrite and simplification capabilities are sometimes a
bit limited.


Michael.