Question

SinA/1-cotA+cosA/1-tanA​=sinA+cosA

Answer 1

Answer:

Step-by-step explanation:

CosA1–SinA+SinA1−CotA=SinA+CosA

LHS = CosA1–SinA+SinA1−CotA LHS=CosA1−SinACosA+SinA1−CosASinA LHS=Cos2ACosA–SinA+Sin2ASinA–CosA LHS=Cos2A–Sin2ACosA–SinA LHS=(CosA+SinA)(CosA–SinA)CosA–SinA LHS=(CosA+SinA) = RHS

LHS = RHS

Answer 2

$\frac{sinA}{1 - cotA} + \frac{cosA}{1 - tanA} \\ \\ = \frac{ {sin}^{2}A }{sinA - cosA} + \frac{ {cos}^{2}A }{cosA - sinA} \\ \\ = \frac{ {sin}^{2}A }{sinA - cosA} - \frac{ {cos}^{2} A}{sinA - cosA} \\ \\ = \frac{ {sin}^{2}A - {cos}^{2} A}{sinA - cosA} \\ \\ = sinA + cosA$