English, asked by saratchandrakum1609, 1 year ago

SinA(1+tanA) +cosA(1+cotA)

Answers

Answered by Declspec
0

Answer:

\frac{sinA + cosA}{sinAcosA}

Explanation:

sinA(1 + tanA) + cosA(1 + cotA)

⇒ sinA(1 + \frac{sinA}{cosA}) + cosA(1 + \frac{cosA}{sinA})

⇒ sinA + \frac{sin^{2}A}{cosA} + cosA + \frac{cos^{2}A}{sinA}

Taking LCM:

\frac{sin^{3}A + cos^{3}A + sinA^{2}cosA + sinAcos^{2}A}{sinAcosA}

\frac{(sinA + cosA)(sin^{2}A + cos^{2}A - sinAcosA) + sinA^{2}cosA + sinAcos^{2}A}{sinAcosA}      

\frac{(sinA + cosA)(1 - sinAcosA) + sinA^{2}cosA + sinAcos^{2}A}{sinAcosA}

\frac{sinA + cosA - sin^{2}AcosA - sinAcos^{2}A + sinA^{2}cosA + sinAcos^{2}A}{sinAcosA}

\frac{sinA + cosA}{sinAcosA}

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