If cos 2θ = 0.28 then, find the value of expression :- (cosecθ – t

1.	If cos 2θ = 0.28 then, find the value of expression :- (cosecθ – tanθ + sinθ)/(cosecθ + tanθ + sinθ) 1. 12. 0.753. 0.5034. 0.50
Answer» Correct Answer - Option 3 : 0.503 Given: cos 2θ = 0.28 Concepts used: cos 2θ = 2 cos²θ - 1 Pythagoras theorem: H2 = P2 + B² cosθ = B/H, cosecθ = H/P, tanθ = P/B, sinθ = P/H Calculation: ⇒ cos 2θ = 2 cos2θ - 1 ⇒ 0.28 = 2 cos2θ - 1 ⇒ 2 cos2θ = 0.28 + 1 ⇒ 2 cos2θ = 1.28 ⇒ cos2θ = 0.64 ⇒ cosθ = √0.64 ⇒ cosθ = 0.8/1 As cosθ = Base/hypotenuse ⇒ 0.8 = Base/hypotenuse On comparing, Base (B) = 0.8, hypotenuse (H) = 1 Using Pythagoras theorem, H2 = P2 + B² ⇒ 1² = P² + (0.8)² ⇒ 1 = P² + 0.64 ⇒ 1 - 0.64 = P² ⇒ P² = 0.36 ⇒ P² = √0.36 ⇒ P = 0.6 Value of sinθ = P/H ⇒ 0.6/1 ⇒ 0.6 Value of cosecθ = H/P ⇒ 1/0.6 ⇒ 1.67 Value of tanθ = P/B ⇒ 0.6/0.8 ⇒ 0.75 Value of expression, (cosecθ - tanθ + sinθ)/(cosecθ + tanθ + sinθ) = (1.67 - 0.75 + 0.6)/(1.67 + 0.75 + 0.6) ⇒ 1.52/3.02 ⇒ 0.503 ∴ The value of the expression is 0.503.

If cos 2θ = 0.28 then, find the value of expression :- (cosecθ – tanθ + sinθ)/(cosecθ + tanθ + sinθ) 1. 12. 0.753. 0.5034. 0.50

Answer» Correct Answer - Option 3 : 0.503

Given:

cos 2θ = 0.28

Concepts used:

cos 2θ = 2 cos²θ - 1

Pythagoras theorem:

H2 = P2 + B²

cosθ = B/H, cosecθ = H/P, tanθ = P/B, sinθ = P/H

Calculation:

⇒ cos 2θ = 2 cos2θ - 1

⇒ 0.28 = 2 cos2θ - 1

⇒ 2 cos2θ = 0.28 + 1

⇒ 2 cos2θ = 1.28

⇒ cos2θ = 0.64

⇒ cosθ = √0.64

⇒ cosθ = 0.8/1

As cosθ = Base/hypotenuse

⇒ 0.8 = Base/hypotenuse

On comparing, Base (B) = 0.8, hypotenuse (H) = 1

Using Pythagoras theorem,

H2 = P2 + B²

⇒ 1² = P² + (0.8)²

⇒ 1 = P² + 0.64

⇒ 1 - 0.64 = P²

⇒ P² = 0.36

⇒ P² = √0.36

⇒ P = 0.6

Value of sinθ = P/H

⇒ 0.6/1

⇒ 0.6

Value of cosecθ = H/P

⇒ 1/0.6

⇒ 1.67

Value of tanθ = P/B

⇒ 0.6/0.8

⇒ 0.75

Value of expression, (cosecθ - tanθ + sinθ)/(cosecθ + tanθ + sinθ) = (1.67 - 0.75 + 0.6)/(1.67 + 0.75 + 0.6)

⇒ 1.52/3.02

⇒ 0.503

∴ The value of the expression is 0.503.