Question

The value of √sec^2 theta -1 =​

Answer 1

Answer:

Divide the terms on the numerator by

sec

2

θ

⇒

sec

θ

−

1

sec

2

θ

=

sec

2

θ

sec

2

θ

−

1

sec

2

θ

and 'simplifying' :

1

−

cos

2

θ

=

sin

2

θ

Answer 2

Answer:

The value of √( sec²θ - 1 ) is tan θ .

Step-by-step explanation:

Given that :

$\sqrt{ ( { \sec}^{2}θ - 1) }$

Solution :

• We know that, sec θ = 1/cos θ.
• Putting this in above equation, we get;

$\sqrt{ \frac{1}{ { \cos }^{2}θ } - 1 } = \sqrt{ \frac{1 - { \cos }^{2}θ }{ { \cos }^{2} θ} } \\ also \: \: \: \: \: { \sin }^{2}θ + { \cos}^{2}θ = 1 \\ or \: \: \: 1 - { \cos }^{2} θ = { \sin }^{2}θ \\ putting \: this \: value \: we \: get \\ \sqrt{ \frac{ { \sin }^{2}θ}{ { \cos }^{2}θ} } = \sqrt{ { \tan}^{2}θ} = \tan(θ)$

• Hence, √( sec²θ - 1 ) = tan θ .