Question

sin(45)/cot(45) * sin(90) + tan(30)/cos(90) +
cosec(60)/sec(45) + sin(90) + tan(60) + cot(45) + sec(45) + cos(45) + sin(45) = ???

Answer 1

To begin, let's keep order of operations in mind. Let's also have a unit circle nearby:

Sin(45)/Cot(45) * Sin(90) + Tan(30)/Cos(90) + Csc(60)/Sec(45) + Sin(90) + Tan (60) + Cot(45) + Sec(45) + Cos(45) + Sin(45)

Take a look at the first quotient; we can simplify that using a reciprocal identity for Cotangent.

Sin(x)/Cot(x) = Sin(x)/1 * Cos(x)/Sin(x) = Cos(x)

Also, according to the unit circle, Sin(90) = 1.

So: Sin(45)/Cot(45) * Sin(90) = Cos(45), which, according to the unit circle is \[\sqrt{2}/2\]

Tan(30)/Cos(90) presents a problem though because Cos(90) is 0.

With an undefined piece in the question, I believe the whole answer would then become undefined.

Answer 2

thanks , is this question wrong???

Answer 3

I would double check that it was copied down correctly. That division by Cos(90) is messing things up.