Prove that- tan A- A- A A

tan A+ A =sin Acos A+cos Asin A =sin^2 A+cos^2 Asin Acos A =1sin Acos A =1sin A×1cos A #160; = A #160; A tan A+ A= ...

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Standard XII

Mathematics

General Solution of Trigonometric Equation

Prove that: ...

Question

Prove that: $tan A + cot A = sec A csc A$

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Solution

$tan A + cot A$

$= \frac{sin A}{cos A} + \frac{cos A}{sin A}$

$= \frac{{sin}^{2} A + {cos}^{2} A}{sin A cos A}$

$= \frac{1}{sin A cos A}$

$= \frac{1}{sin A} \times \frac{1}{cos A}$

$= csc A$ $sec A$

$tan A + cot A = sec A csc A$

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Prove that: tanA+cotA=secAcscA

tanA+cotA=sinAcosA+cosAsinA=sin2A+cos2AsinAcosA=1sinAcosA=1sinA×1cosA=cscA secAtanA+cotA=secAcscA

Prove that: $tan A + cot A = sec A csc A$

$tan A + cot A$

$= \frac{sin A}{cos A} + \frac{cos A}{sin A}$

$= \frac{{sin}^{2} A + {cos}^{2} A}{sin A cos A}$

$= \frac{1}{sin A cos A}$

$= \frac{1}{sin A} \times \frac{1}{cos A}$

$= csc A$ $sec A$

$tan A + cot A = sec A csc A$