How do you solve (sec^2)+(tan^2)+6 with trig identities?

Question

how do you solve this without using a calculator.**strictly trig identities

Answer 1

Let θ is an angle.

sec²θ + tan²θ + 6.

Pythagorean Identities: sec²θ = 1 + tan²θ

1 + tan²θ + tan²θ + 6.

2tan²θ + 7.

 

or

Let θ is an angle.

sec²θ + tan²θ + 6.

Pythagorean Identities: tan²θ = sec²θ - 1

sec²θ + sec²θ - 1 + 6

2sec²θ + 5.