Question

x = a cos theta + b sin theta, y = b cos theta - a sin theta. eliminate theta from the equation.

please don't give unnecessary answers. ​

Answer 1

Answer:

⭐⭐⭐⭐⭐ ANSWER ⭐⭐⭐⭐⭐

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❄❄❄❄ EXPLANATION ❄❄❄❄

➡ In first numerical and also in second numerical, we had find the values of sec theta and tan theta [IN QUESTION 1], cos theta and sin theta [IN QUESTION 2].

➡ Then we apply trigonometric formulas immediately.

➡ In first numerical, sec²theta-tan²theta=1.

➡ In second numerical, sin²theta+cos²theta=1.

➡ Thus, the thetas got eliminated and our answer becomes ready.

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⭐⭐⭐ ALWAYS BE BRAINLY ⭐⭐⭐

if help needed refer to https://brainly.in/question/7274717

Step-by-step explanation:

Answer 2

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$\: \: \large \green {\bold{ \underline{ \underline{ \star answer : }}}}$

$\: \bullet\bold{ \underline{x = a cos \theta \: + bsin \theta \: \: and \: \: \: y = bcos \theta \: - asin \theta}} \: \\ \underline{ \bf{estimate \theta \: from \: the \: equation}}$

$\: \: \large \blue {\bold{ \underline{ \underline{given \: equation : }}}}$

$\: \bullet \bold{x = acos \theta \: + bsin \theta..........equation(1)}$

$\: \bullet \bold{x = bcos \theta - asin \theta........equation(2)}$

$\: \: \star \red {\bold{ \underline{ \underline{ \: squaring \: both \: equation \: (1) \: and \: (2)}}}}$

$\: \bullet \bold{ {x}^{2} = ( {acos \theta + bsin \theta)}^{2} }$

$\: \\ \to \bold{ {x}^{2} = {a}^{2} {cos}^{2} \theta + {b}^{2} {sin}^{2} \theta + 2absin \theta cos \theta}...(1)$

$\: \bullet \bold{ {y}^{2} = {(bcos \theta - asin \theta)}^{2} }$

$\\ \to \bold{ {y}^{2} = {b}^{2} {cos}^{2} \theta + {a}^{2} {sin}^{2} \theta - 2abcos \theta sin \theta} ....(2)$

$\: \star \large \blue{ \bold{ \underline{ \underline{adding \: both \: equation \: (1) \: and \: (2)}}}}$

$\: \tt : \implies \: {x}^{2} + {y}^{2} = {a}^{2} {cos}^{2} \theta + {b}^{2} {sin}^{2} \theta + 2abcos \theta sin \theta + {b}^{2} {cos}^{2} \theta + {a}^{2} {sin}^{2} \theta - 2absin \theta cos \theta$

$\tt : \implies {x}^{2} + {y}^{2} = {a}^{2} ( {sin}^{2} \theta + {cos}^{2} \theta) + {b}^{2} ( {sin}^{2} \theta + {cos}^{2} \theta) + 2absin \theta \: cos \theta - 2absin \theta \: cos \theta$

$\tt : \implies {x}^{2} + {y}^{2} = {a}^{2} ( {sin}^{2} \theta + {cos}^{2} \theta) + {b}^{2} ( {sin}^{2} \theta + {cos}^{2} \theta) + \cancel {2abcos \theta \: sin \theta - 2acos \theta \: sin \theta}$

$\: \tt : \implies \: {x}^{2} + {y}^{2} = {a}^{2} (1) + {b}^{2} (1)$

$\: \tt : \implies {x}^{2} + {y}^{2} = {a}^{2} + {b}^{2}$

$\: \bigstar \: \green{\bold {{ \underline{ \underline{ {x}^{2} + {y}^{2} = {a}^{2} + {b}^{2} \: is \: the \: answer}}}}}$