SOLUTION: Simplify without using tables or calculators.sin^2 495degrees(1-tan^2 780degrees/(1 cos^2 600degrees)(1 tan^ 570degrees)

Question 934973: Simplify without using tables or calculators.sin^2 495degrees(1-tan^2 780degrees/(1 cos^2 600degrees)(1 tan^ 570degrees)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I suspect that what you mean may have been
sin^2 (495degrees)(1-tan^2 (780degrees))/(1 - cos^2 (600degrees))(1-tan^2) 570degrees))= ,
but whatever the operations among those trigonometric functions,
the expression's value is much simpler than it looks.
The key is to find a more familiar/convenient co-terminal angle (one that differs by one or more turns in either direction). I aim for one between and .
From there, you look for a reference angle in the first quadrant.
The reference angle is one with a symmetrical terminal side. All trigonometric have the same absolute value for the reference angle, so you just have to worry about the sign. (And if all ther trigonometric functions in your expression are squared, you do not even have to worry about the sign.

so ,
and is an angle in the second quadrant
that is symmetrical to ,
so ,
and

so ,
so ,
and .

so ,
and is an angle in the third quadrant,
that is symmetrical to in the second quadrant,
and to in the first quadrant.
.
Then, and .

and ,
so the reference angle for is ,
and .
Then, and
.

So if your expression was ,

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