simplify expression

Question

sec^2(θ)+2tan^2(θ)/1+3tan^2(θ)

Answer 1

The answer is 1....

multiplying top and bottom by cos^2:

(1 + 2 sin^2 ) over ( cos^2 + 3 sin^2)

(sin^2 + cos^2 + 2sin^2) over ( cos^2 + 3 sin^2) <--- trig identity 1 = sin^2 + cos^2

(3 sin^2 + cos^2) over ( cos^2 + 3 sin^2) <--- combines like terms

which is 1

Answer 2

Recall that 1 + tan²Θ = sec²Θ.

So, sec²Θ + 2tan²Θ = (1 + tan²Θ) + 2tan²Θ = 1 + 3tan²Θ

Since the numerator and denominator of the given expression are identical, the value of the given expression is 1.