If tan²θ = 1 – e² , then the value of

Home » Aptitude » Trigonometry » Question

If tan²θ = 1 – e² , then the value of secθ + tan³θ cosecθ is

1. (2 + e²)^{3 / 2}
2. (2 - e²)^{1 / 2}
3. (2 + e²)^{1 / 2}
4. (2 - e²)^{3 / 2}

Correct Option: D

tan²θ = 1 –e²
∴ secθ + tan³θ . cosecθ
= secθ + tan²θ . tanθ . cosecθ

= secθ + tan²θ .		sin θ	.	1
		cos θ		sin θ

= secθ + tan²θ . secθ
= secθ .(1 + tan²θ)