Question

If sec theta + tan theta =m, then sec^4 theta - tan^4 theta - 2sec theta × tan theta =??

Answer 1

value of sec⁴θ - tan⁴θ - 2secθ.tanθ = 1/m²

given, secθ + tanθ = m .......(1)

we have to find out the value of sec⁴θ - tan⁴θ - 2secθ.tanθ

sec⁴θ - tan⁴θ - 2secθ.tanθ

= (sec²θ + tan²θ)(sec²θ - tan²θ) - 2secθ.tanθ

= (sec²θ + tan²θ) × 1 - 2secθ. tanθ

= sec²θ + tan²θ - 2secθ.tanθ

= (secθ - tanθ)² ........(2)

from trigonometric identity,

sec²θ - tan²θ = 1

⇒(secθ - tanθ)(secθ + tanθ) = 1

⇒(secθ - tanθ) × m = 1 [ from equation (1).]

⇒(secθ - tanθ) = 1/m , put this in equation (2)..

we get, sec⁴θ - tan⁴θ - 2secθ.tanθ = (1/m)² = 1/m²

also read similar questions:If sec theta+tan theta=m, then sec^4 theta-tan^4 theta-2sec theta×tan theta=?

https://brainly.in/question/14458709

sec theta-tan theta upon sec theta + tan theta= 1-2sec theta tan theta +2 tan square theta

https://brainly.in/question/2545553