Prove that cos A1 - tan A - sinA1 - A - cos A - sinA -

LHS=cosA/(1 tanA)+sinA/(1 cotA)=cos A/(1 sin A/cos A) + sin A/(1 cos A/sin A)=cos #178;A/ (cos A sin A) + sin #178;A / (sin A cos A)=cos #178;A/ ( ...

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Byju's Answer

Standard XII

Mathematics

Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

Prove that ...

Question

Prove that $\frac{cos A}{1 - tan A} + \frac{sinA}{1 - cot A} = cos A + sinA .$

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Solution

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

LHS=RHS
Hence, Proved

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Prove that cosA1−tanA+sinA1−cotA=cosA+sinA.

Prove that $\frac{cos A}{1 - tan A} + \frac{sinA}{1 - cot A} = cos A + sinA .$