Question

( sina+cosa)^2- sin2a ​

Answer 1

(sina+cosa)^2-sin2a=1

Answer 2

To simplify the expression $(\sin a + \cos a)^2 - \sin 2a$, let's first expand the square of the binomial $(\sin a + \cos a)^2$ and then simplify the result.

Step 1: Expand $(\sin a + \cos a)^2$

$(\sin a + \cos a)^2 = (\sin a + \cos a)(\sin a + \cos a)$

To expand this, we'll use the distributive property:

$(\sin a + \cos a)(\sin a + \cos a) = \sin a \cdot \sin a + \sin a \cdot \cos a + \cos a \cdot \sin a + \cos a \cdot \cos a$

Step 2: Simplify the expanded expression:

Recall that $\sin^2 a = (\sin a)^2$ and $\cos^2 a = (\cos a)^2$:

$\sin^2 a + \sin a \cos a + \cos a \sin a + \cos^2 a$

Since $\sin a \cos a$ and $\cos a \sin a$ are the same, we can simplify the expression:

$= \sin^2 a + 2 \sin a \cos a + \cos^2 a$

Step 3: Apply the trigonometric identity $\sin^2 a + \cos^2 a = 1$:

$= 1 + 2 \sin a \cos a$

Finally, we can subtract $\sin 2a$ from this simplified expression:

$= 1 + 2 \sin a \cos a - \sin 2a$

And that's the simplified form of the expression $(\sin a + \cos a)^2 - \sin 2a$.