(Sin t + cos t)^2 = ?

Can anyone help me with this question?

The answer to your question is: Yes.
Now, would you like to actually see the solution ?
First, multiply the quantity out:
(sin + cos)² = sin²(t) + cos²(t) + 2sin(t)cos(t)
You need to know: ==> sin²(any angle) + cos²(the same angle) = 1 ==> 2sin(any angle)cos(the same angle) = sin(double the angle)
So the equation becomes:
(sin + cos)² = 1 + sin(2t)

Answered by AL2006 | 2024-06-10

( s in t + cos t ) 2 = s i n 2 t + co s 2 t + 2 ⋅ s in t ⋅ cos t = 1 + s in 2 t

Answered by kate200468 | 2024-06-10

The expression ( sin t + cos t ) 2 simplifies to 1 + sin ( 2 t ) by expanding the square and using trigonometric identities. First, you expand, then apply the identity sin 2 t + cos 2 t = 1 , and finally use the double angle identity sin ( 2 t ) = 2 sin t cos t .
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Answered by AL2006 | 2024-12-23