Question

if 4cos² thita - 1 = 0 find the acute angle thita hnece find the value of 2tan thita / 2tan² thita ​

Answer 1

Answer:

thetta = 60°

2tanthetta/2tan²thetta = 2 root3/6

Step-by-step explanation:

4cos²thetta-1=0

4cos²thetta=1

cos²thetta=1/4

costhetta =1/2

therefore thetta =60°

2tanthetta/2tan²thetta

2×root3/2×(root3)²

2root3/6

Answer 2

Step-by-step explanation:

Given:-

4cos² thita - 1 = 0

To find:-

if 4cos² thita - 1 = 0 find the acute angle thita hence find the value of 2tan thita / 2tan² thita

Solution:-

Given equation is 4 Cos^2 θ -1 = 0

=>4 cos^2 θ = 1

=>Cos^2 θ = 1/4

=>Cos θ = √(1/4)

=>Cos θ = 1/2

• => Cos θ = Cos 60°

Therefore, θ = 60°

The value of the acute angle θ = 60°

The value of 2 tan θ/ 2 tan^2 θ

=>2 Tan 60° / 2 tan^2(60°)

=>2 (√3) /2(√3)^2

=>2√3/(2×3)

=>2√3/6

=>√3/3 (0r)

=>√3/(√3×√3)

=>1/√3

or

2 tan θ/ 2 tan^2 θ

=>2 Tanθ/2 tanθ×tanθ

=>1/tanθ

=>Cotθ

=>Cot60°

=>1/√3

Answer:-

The value of an acute angle θ = 60°

The value of 2 tan θ/ 2 tan^2 θ = √3/3 or 1/√3

Used formula:-

• Cos 60° = 1/2
• Tan 60°= √3
• Cot 60°= 1/√3
• 1/TanA = Cot A