Question

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Answer 1

$\bold{\huge{\fbox{\color{Maroon}{Hope It Helps You}}}}$

Answer 2

Question :

The area of triangle whose vertices are ( acosθ , bsinθ ) , ( - asinθ , bcosθ )

and ( - acosθ , - bsinθ ) is :

OPTION A : absinθcosθ

OPTION B : acosθsinθ

OPTION C : 1/2 ab

OPTION D : ab

Answer:

OPTION D

Step-by-step explanation:

Given :

x₁ = acosθ

x₂ = -asinθ

x₃ = -acosθ

y₁ = bsinθ

y₂ = bcosθ

y₃ = -bsinθ

$\mathsf{Area=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|}\\\\\implies \mathsf{Area=\dfrac{1}{2}|acos\theta(bcos\theta+bsin\theta)+(-asin\theta)(-bsin\theta-bsin\theta)+(-acos\theta)(bsin\theta-bcos\theta)|}\\\\\implies \mathsf{Area=\dfrac{1}{2}|abcos^2\theta+absin\theta cos\theta+2absin^2\theta-abcos\theta sin\theta+abcos^2\theta|}\\\\\implies \mathsf{Area=\dfrac{1}{2}|2abcos^2\theta+2absin^2\theta|}\\\\\implies \mathsf{Area=\dfrac{1}{2}|2ab(cos^2\theta+sin^2\theta)|}$

$\bf{Use\:sin^2\theta+cos^2\theta=1}\\\\\implies \mathsf{Area=\dfrac{1}{2}|2ab\times1|}\\\\\implies \mathsf{Area=\dfrac{1}{2}\times 2ab}\\\\\implies \mathsf{Area=ab}$

Hence the option D is the correct option .