If sec\(^2\)θ + tan\(^2\)θ = 3, then the angle θ is equal to?

Dolapo235

2 years ago

The correct answer is C. 45º.

Here's a brief explanation:

sec2θ + tan2θ = 3

Using the Pythagorean identity, we can rewrite this as:

sec2θ + (sec2θ - 1) = 3

Combine like terms:

2sec2θ - 1 = 3

Add 1 to both sides:

2sec2θ = 4

Divide both sides by 2:

sec2θ = 2

Take the square root of both sides:

secθ = √2

Using the definition of secant, we can write:

1/cosθ = √2

This is true when θ = 45º (or π/4 radians).

So, the correct answer is C. 45º.

mercy12345678ush

1 year ago

R