Question

Use basic identities to simplify the expression. one divided by cotangent of theta to the second power. + sec θ cos θ

Answer 1

please help me! I am taking precalc online and don't understand a single thing about basic identities

Answer 2

so its
\(\huge \dfrac{1}{\cot^2 \theta + \sec \theta \cos \theta} \)

Answer 3

firstly, use the identity that sec theta = 1/cos theta
so,
sec theta cos theta = 1

and do you know what is \(\large 1+\cot^2 \theta = ... ?\)

Answer 4

only the cot^2theta is the denominator

Answer 5

no I don't know, I am COMPLETELY lost in this subject

Answer 6

okk.,
so anyways you can use sec theta cos theta = 1
\(\large \dfrac{1}{\cot^2 \theta }+1 \)

Answer 7

now 1/ cot theta = tan theta
so,
\(\large \tan^2 \theta+1 \)

Answer 8

and ther's a standard pythagorean identity that
\(\large 1+\tan^2 \theta = \sec^2 \theta \)
thats it! :)

Answer 9

okay thank you!

Answer 10

can you walk me through another please?

Answer 11

sure

Answer 12

Simplify the expression.

quantity cosecant of x to the power of two times secant of x to the power of two divided by quantity secant of x to the power of two plus cosecant of x to the power of two.