Question

(sin ø- cos ø)²+(sin ø- cos ø)²=​

Answer 1

Answer:

$\displaystyle \sf{ \red{ \bold{ Find}}}$

${ \sf{➣( {sinθ - cosθ)}^{2} + {(sin θ- cosθ)}^{2} }}$

${ \bold{ \blue{Solution}}}$

${ \sf{⟶ {(sinθ - cosθ)}^{2} + {(sinθ - cosθ)}^{2} }}$

From, Algebraic formula.....

${ \boxed{ \bold{ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}}}$

${ \sf{⟶ {sin}^{2}θ + {cos}^{2} θ - 2sinθcosθ + {sin}^{2} θ + {cos}^{2} θ - 2sinθcosθ}}$

From trigonometry identity:-

${ \boxed{ {sin}^{2} + {cos}^{2} = 1 }}$

${ \sf{⟶1 - 2sinθcosθ + 1 - 2sinθcosθ}}$

${ \sf{⟶2 - 4sinθcosθ}}$

Therefore, (sin θ- cos θ)²+(sin θ- cos θ)²=2-4sinθcosθ