If sec² ø + tan² ø = 25/18 , than the value of sec⁴ø - tan⁴ø is:

If sec² ø + tan² ø = 25/18 , than the value…

If sec² ø + tan² ø = $\frac{25}{18}$ , than the value of sec⁴ø - tan⁴ø is:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. $\frac{25}{18}$ .

Given that

If sec² ø + tan² ø = $\frac{25}{18}$

the value of sec⁴ø - tan⁴ø

⇒ sec⁴ø - tan⁴ø

⇒ (sec² ø + tan² ø) (sec² ø - tan² ø)

As we know,

sec² ø - tan² ø = 1

So,

⇒ $\frac{25}{18}$ × 1

⇒ $\frac{25}{18}$