Question

(sin³A+cos³A/SinA+CosA)+sinA.CosA​

Answer 1

Solution -

$\sf{ \: \dfrac{ { \sin{a} }^{3} + { \cos{a} }^{3} \: }{ \sin{a} \: + \cos{a} } \: } + \sin{a} . \cos{a} \\ \\ = > \dfrac{( \cancel{\: \sin{a}+ \cos{a} \:} )( {\sin{a}}^{2} + {\cos{a}}^{2} - \sin{a} . \cos{a}) }{ \cancel{\sin{a} \: + \cos{a} \: }} + \sin{a} . \cos{a} \: \\ \\ = > {\sin{a}}^{2} + {\cos{a}}^{2} - \cancel{ \sin{a} . \cos{a} } \: + \: \cancel{\sin{a} . \cos{a} }\\ \\ = > {\sin{a}}^{2} + {\cos{a}}^{2} \: \\ \\ = > 1 \: .........[ A ]$

$\sf{ Additional \: Information \: :- } \\ \\ \circ{\sf{\: \: {\sin{a}}^{2} + {\cos{a}}^{2} = 1 }} \\ \\ \circ{\sf{ \: \: {\sec{a}}^{2} = 1 + {\tan{a}}^{2} }} \\ \\ \circ{\sf{ \: \: { \csc{a}}^{2} = 1 + {\cot{a}}^{2} }}$

Answer 2

Answer:

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