Question

Sec²theta-tan²theta=1​

Answer 1

Answer:

Answer:- Yes Sec²θ - tan²θ

$\frac{ \cos {}^{2}θ \: + \: \: \sin{}^{2} θ }{ \sin {}^{2}θ \: \: \times \: \: \cos {}^{2}θ }$

= 1.

Step-by-step explanation:

${\boxed{\tt{Verification\::-}}}$

$\sec {}^{2} θ = \frac{1}{ { \cos }^{2} θ}$

$\tan{}^{2} θ = \frac{ \sin {}^{2}θ }{ \cos{}^{2} θ}$

No Putting these Formulaes in Equation.

We Get,

$\frac{1}{ { \cos }^{2} θ} - \frac{ \sin{}^{2} θ }{ { \cos }^{2} θ}$

Here is a Formula will be applied.

i.e., sin²θ + cos²θ = 1

So We can say Cos²θ = 1 - Sin²θ

$\frac{ 1 - \sin {}^{2} θ }{ \cos {}^{2} θ }$

From Above Equation that i have highlighted will be applied now:-

$\frac{ \cos {}^{2} θ }{ \cos {}^{2} θ } = 1$

After Cancellation The remaining value is 1. So it's proved that Sec²θ - tan²θ = 1

${\boxed{\tt{Proved\:!!}}}$

Answer 2

Answer:

Sec^2-Tan^2=1 hence proved