Question

$If \\ \\ sec \ \theta + tan \ \theta = \frac{7}{5}, \\ \\ then, \\ \\ sec \ \theta - tan \ \theta = \ ?$

Answer 1

Answer:

secθ - tanθ = 5/7

Step-by-step explanation:

Given, secθ + tanθ = 7/5

We know that sec²θ - tan²θ = 1.

⇒ (secθ + tanθ)(secθ - tanθ) = 1

⇒ (7/5)(secθ - tanθ) = 1

⇒ (secθ - tanθ) = 5/7

Therefore, secθ - tanθ = 5/7

Hope it helps!

Answer 2

given,

sec θ+tan θ=7​/5

we know,

${a}^{2} - {b}^{2} = (a + b) \times (a - b)$

${ \sec( \alpha ) }^{2} - { \tan( \alpha ) }^{2} = 1 \\ = > ( \sec( \alpha) + \tan( \alpha ) ) \times ( \sec( \alpha ) - \tan( \alpha ) ) \\ = > 1 = \frac{7}{5} \times \sec( \alpha ) - \tan( \alpha ) \\ = > \sec( \alpha ) - \tan( \alpha ) = \frac{5}{7}$

Thanks

KSHITIJ