Question

If sin theeta + cos theeta =1

then sin theeta cos theeta =​

Answer 1

Step-by-step explanation:

$\huge\bf{\mid{\overline{\underline{ANSWER}\mid}}}$

$\\ \\ \huge\bold{Given:-} \\ \\ \sin(\Theta) + \cos(\Theta) = 1 \\ \\ \huge\bold{To \: \: find:-} \\ \\ \sin(\Theta) \times \cos(theta) = ? \\ \\ \\ \implies \sin(\Theta) + \cos(\Theta) = 1 \\ \\ \implies ({\sin(\Theta) + \cos(\Theta)})^{2} = {1}^{2} \\ \\ \implies {\sin}^{2}(\Theta) + {\cos}^{2}(\Theta) + 2 \sin(\Theta) \times \cos(\Theta) = 1 \\ \\ We \: \: know, \boxed{\sin(\Theta) + \cos(\Theta) = 1 } \\ \\ So \: \: using \: \: this..\\ \\ \implies {\sin}^{2}(\Theta) + {\cos}^{2}(\Theta) + 2 \sin(\Theta) \times \cos(\Theta) = 1 \\ \\ \implies 1 + 2 \sin(\Theta) \times \cos(\Theta) = 1 \\ \\ \implies 2 \sin(\Theta) \times \cos(\Theta) = 1 - 1 \\ \\ \implies 2 \sin(\Theta) \times \cos(\Theta) = 0 \\ \\ \huge\boxed{ \implies \sin(\Theta) \times \cos(\Theta) = 0}$

Answer 2

AnswEr :

Sin theeta + Cos theeta = 1

Squaring both sides

(Sin theeta + Cos theeta)² = 1²

Now it is in the form ( a+b)²

So, By using Identify (a + b)² = a² + b² + 2ab

=> Sin²theeta + Cos ²theeta + 2SinCos theeta = 1

We know the Identity Sin²theeta + Cos²theeta = 1

= 1 + 2Sin theeta Cos theeta=1

= 2Sin theeta Cos theeta = 0

= Sin theeta Cos theeta =0