Question

If tan theta + sec(theta) = n , then sec^4 theta - tan^4 theta - 2

sec theta * tan theta =

Answer 1

Answer:

Step-by-step explanation:

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)..