Question

Verify the identity.
cot θ ∙ sec θ = csc θ

Answer 1

I'm not exactly sure what it's asking me to do

Answer 2

ok... so

cot = 1/tan and tan = sin/cos

which means cot = cos/sin

and sec = 1/cos

so substitute cot = cos/sin and sec = 1/cos

and you get

\[\frac{\cos(x)}{\sin(x)} \times \frac{1}{\cos(x)} \]

cancel the common factor and you're left with

\[\frac{1}{\sin(x)}\]

so how do you think csc(x) can be written using sin, cos or tan..?

Answer 3

I really have no idea

Answer 4

@ganeshie8 Can you help me please?

Answer 5

\(\bf {\color{blue}{ cot(\square )=\cfrac{cos(\square )}{sin(\square )}\qquad \qquad sec(\square )=\cfrac{1}{cos(\square )}}}\\ \quad \\ \quad \\

cot(\theta)\cdot sec(\theta)=csc(\theta)\\ \quad \\
\implies \cfrac{cos(\theta )}{sin(\theta )}\cdot \cfrac{1}{cos(\theta )}\)

Answer 6

So would this be the final answer?

Answer 7

well... what did you get?

Answer 8

can you simplify it further?

Answer 9

Do I put that in my calc?

Answer 10

well, you're just expected to make the LEFT-SIDE look like the RIGHT-SIDE, is all

Answer 11

Ohhhh okay. Thank you!

Answer 12

yw

Answer 13

And if I'm correct

csc θ = 1/sinθ