If sec² θ + tan² θ = 3 1/2 , 0° < θ < 90°, then (cosθ + sinθ) is equal to

If sec² θ + tan² θ = 3 1/2 , 0° < θ < 90°, then (cosθ +…

If sec² θ + tan² θ = 3 $\frac{1}{2}$ , 0° < θ < 90°, then (cosθ + sinθ) is equal to

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Correct answer: A

Explanation

The correct answer is option 1 i.e.

Formula used:

sec² θ - tan² θ = 1 ----- (1)

Calculations:

sec² θ + tan² θ = 3(1/2) ---- (2)

Solving equation (1) and (2), we get

sec θ = 3/2 = Hypotenuse/perpendicular

Using Pythagoras theorem,

⇒ 3² = 2² + Base²

⇒ Base² = 5

⇒ Base = √5

According to the question:

⇒ cosθ + sinθ

⇒ 2/3 + √5/3 = (2 + √5)/3