Question

Tan^2x=csc^2xtan^2x-1

Answer 1

lets simpilfy csc^2x tan^2x

\(\huge\color{blue}{\sf \frac{1}{sin^2x} \times \frac{sin^2x}{cos^2x} }\)

\(\huge\color{blue}{\sf \frac{1 \times sin^2x}{ sin^2x\times cos^2x} }\)

\(\huge\color{blue}{\sf \frac{1 \times sin^2x}{ sin^2x\times cos^2x} }\)

\(\huge\color{blue}{\sf \frac{1 \times \cancel{ ( sin^2x ) } }{ \cancel{ ( sin^2x ) } \times cos^2x} }\)

\(\huge\color{blue}{\sf \frac{1}{ cos^2x} }\)

Answer 2

and we know that 1/ cos^2x = sec^2x

So, you end up getting

\(\huge\color{purple}{\sf Tan^2x=Sec^2x-1 }\)

which is an identity.

IF you had to solve for x, then there is an infinite number of solutions.
if you had to prove an identity, it's verified and identity.

Answer 3

Thank you .

Answer 4

\(\huge\color{forestgreen}{\sf Anytime~! }\)