Question

Complete the identity. tan^2(x)-3sin(x)tan(x)sec(x)

Answer 1

is there supposed to be an equal sign somewhere?

Answer 2

Well technically after all of that, yes. The possible options on this multiple choice are -2tan^2, 1+cot, sintan, or seccsc. I'm so confused with this one for some reason! I'd greatly appreciate your help

Answer 3

\(\bf tan^2(x)-3sin(x){\color{blue}{ tan(x)sec(x)}}\implies tan^2(x)-3sin(x)\cdot {\color{blue}{ \cfrac{sin(x)}{cos(x)}\cdot \cfrac{1}{cos(x)}}}\\ \quad \\

tan^2(x)-\cfrac{3sin^2(x)}{cos^2(x)}\implies tan^2(x)-3tan^2(x)\)

and you'd see which one is it

Answer 4

hmm got a bit truncated.. anyhow \(\bf tan^2(x)-3sin(x){\color{blue}{ tan(x)sec(x)}}\\ \quad \\\implies tan^2(x)-3sin(x)\cdot {\color{blue}{ \cfrac{sin(x)}{cos(x)}\cdot \cfrac{1}{cos(x)}}}\\ \quad \\

tan^2(x)-\cfrac{3sin^2(x)}{cos^2(x)}\implies tan^2(x)-3tan^2(x)\)

Answer 5

Aw! Thank you so much! Sometimes seeing problems done out like you did helps with others as well.

Answer 6

yw