Question

cos theta = sin 2 theta, then theta=​

Answer 1

Answer:

30 degrees

Step-by-step explanation:

Cos 30= sin2(30)

Answer 2

Step-by-step explanation:

Given:-

Cos θ= Sin 2θ

To find:-

The value of θ ?

Solution:-

Given equation is Cos θ= Sin 2θ

1)

We know that Cos A = Sin (90-A)

=> Sin (90-θ) = Sin 2θ

=>90 - θ = 2θ

=>90 = 2θ+θ

=>90 = 3θ

=>3θ = 90

=>θ = 90/3

=>θ = 30°

(or)

2)

We know that Sin A = Cos (90-A)

=>Cos θ = Cos (90-2θ)

=>θ = 90-2θ

=>θ + 2θ = 90

=>3θ = 90

=>θ = 90/3

=>θ = 30°

(or)

π=180°

=>30° =180°/6 = π/6

π/6 =30°

The value of θ = 30° or π/6 for the given problem

Check:-

If θ = 30° then LHS

=>Cos θ

=>Cos 30°

=>√3/2

RHS :-

Sin2θ

=>Sin 2(30°)

=>Sin 60°

=>√3/2

LHS = RHS is true for θ = 30°

Used formulae:-

• Cos A = Sin (90-A)
• Sin A = Cos (90-A)
• π=180°
• π/6 =30°
• Cos 30° =√3/2
• Sin60° = √3/2