Cosa/1-tana + sina/1-cota=sina+cosa
Answers
LHS
=cosA/(1-tanA)+sinA/(1-cotA)
=cos A/(1 - sin A/cos A) + sin A/(1 - cos A/sin A)
=cos²A/ (cos A - sin A) + sin²A / (sin A - cos A)
=cos²A/ (cos A - sin A) - sin²A / (cos A - sin A)
=(cos ² A - sin ² A) / (cos A - sin A)
=(cos A - sin A)(cos A + sin A) / (cos A - sin A)
=cos A + sin A i.e RHS
Answer:
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Madline
Madline
28.07.2017
Math
Secondary School
+5 pts
Answered
Show that cosA/ 1-tanA+sinA/1-cotA=cosA +sinA
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LHS
=cosA/(1-tanA)+sinA/(1-cotA)
=cos A/(1 - sin A/cos A) + sin A/(1 - cos A/sin A)
=cos²A/ (cos A - sin A) + sin²A / (sin A - cos A)
=cos²A/ (cos A - sin A) - sin²A / (cos A - sin A)
=(cos ² A - sin ² A) / (cos A - sin A)
=(cos A - sin A)(cos A + sin A) / (cos A - sin A)
=cos A + sin A i.e RHS
Step-by-step explanation:
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