Trigonometry

Why 2sin²acos²a = (1/2)sin²a?

I know 2sinacosa = sin 2a but then I am confused why 2 sin²acos²a = (1/2)sin²a.

Thank you.

Reply 1

Speleo

2 sin^2 a cos^2 a = (1/2)(2 sin a cos a)(2 sin a cos a)
= (1/2)(sin^2 2a)

Reply 2

phys981

Civ-217

Why 2sin²acos²a = (1/2)sin²a?

I know 2sinacosa = sin 2a but then I am confused why 2 sin²acos²a = (1/2)sin²a.

Thank you.

Are you sure you've typed that right?

I got 2 sin²acos²a = (1/2)sin²2a.

Reply 3

Civ-217

Oh I see thanks! No I didn't type wrongly.

If a question asks:

By sketching a suitable pair of graphs, show that the equation
2cot x = 1 + e^x ,
where x is in radians, has only one root in the interval 0<x<(pi/2).

Do we let f(x) = 2cot x = 1 + e^x
x |
f(x) |

Then by having some pair values which we will find ourselves and use this to sketch the graph? But then how do we know this equation has only one root in the interval 0<x<(pi/2)?

Thanks!

Reply 4

phys981

Civ-217

Oh I see thanks! No I didn't type wrongly.

Speleo and I both arrived at (1/2)(sin^2 2a) or (1/2)sin²2a

SO if you didn't type wrongly, that answer is wrong,

have you managed to do it differently?

Reply 5

steffy6

Why is Sin²2a=(sin²a*cos²a)²?

Reply 6

simon0

Original post by steffy6

Why is Sin²2a=(sin²a*cos²a)²?

It is not best thing to use an eleven year old thread for your question.

It is best to create a new thread for your question, however, the identities are not equal (try a=