Question

If tanθ = 1/3 , the value of 3sin2θ + cos2θ is

Answer 1

➲ Correct Question :-

⦿ If tanθ = 1/3 , find the value of 3 sin²θ + cos²θ.

➲ Given :-

◑ tan∅ = 1/3

➲ To Find :-

◑ 3 sin²∅ + cos²∅

➲ Solution :-

we know,

⦿ tan ∅ = (perpendicular) / (base)

so, let :-

◑ perpendicular = 1 units

◑ base = 3 units

By applying Pythagoras theorem :-

◑ (Hypotenuse)² = (Base)² + (Perpendicular)²

✒ H² = (3)²+(1)²

✒ H² = 10

∴ H = √10

❒ Hence, Hypotenuse = √10 units

Now,

◑ sin∅ = (perpendicular) / (Hypotenuse)

∴ sin∅ = (1/√10) units

◑ cos∅ = (base) / (Hypotenuse)

∴ cos∅ = (3/√10) units

➽ Now, By Calculation :-

◑ 3 sin²∅ + cos²∅

✒ 3× ( 1/√10)² + (3/√10)²

✒ 3× (1/10) + (9/10)

✒ (3/10) + (9/10)

✒ 12/10

∴ 6/5

➲ Answer :-

◑ The value of 3 sin²θ + cos²θ is 6/5