Question

Quick questions: What is cos multiplied by cos and what is cos divided by cos

Answer 1

let cos = x
now what's x times x and what is x divided by x ?

Answer 2

x^2

Answer 3

x divided by x equals 1?

Answer 4

right
so cos times cos would be \(\large\rm {cos^2 \theta}\)

Answer 5

\[\rm \sin^2 \theta +\cos^2 \theta =1\]
this is a special identity
which can be written as \[\cos^2 \theta = 1-\sin^2 \theta\]
so to verify identity you can replace cos^2 with 1-sin^2

Answer 6

eh but that wasn't your question
and yes x/x =1 so cos/cos =1

Answer 7

and does the same principle apply to sin also?

Answer 8

we are using exponent rules here \[\rm \huge\rm x^m \times x^n =x^{m+n}\]
multiply same bases so add their exponents \[\huge\rm \frac{ x^m }{ x^n }=x^{m-n}\]
when we divide same bases we should subtract their exponents

Answer 9

and yes right sin is same as sin to the one power \[\frac{ \sin^1 }{ \sin^1 } =\sin^{1-1} = \sin^{0}=\sin \theta\]
anything to the zero power equal to one

Answer 10

and when we multiply same bases \[\huge\rm sin^{1} *\sin^{1} =sin^{1+1}=sin^{2} theta \]

Answer 11

wait, sin/sin=sin?

Answer 12

same thing just like cos

Answer 13

what would you get when you divide same bases ?

Answer 14

like 2/2 ,5/5 y/y