Prove that
=Sin 2A/1-Cos2A = cos A
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hey mate hope this helps
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Answered by
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Answer:
jGiven
LHS =\frac{sin2A}{1-cos2A}
1−cos2A
sin2A
= \frac{sin2A}{(cos^{2}A+cos^{2})-(cos^{2}A-sin^{2}A)}
(cos
2
A+cos
2
)−(cos
2
A−sin
2
A)
sin2A
/* Since ,
i) 1 = cos²A + sin²A
ii ) cos2A = cos²A-sin²A */
= \frac{2sinAcosA}{sin^{2}A+cos^{2}A-cos^{2}A+sin^{2}A}
sin
2
A+cos
2
A−cos
2
A+sin
2
A
2sinAcosA
/* we know that,
sin2A = 2sinAcosA */
= \frac{2sinAcosA}{2sin^{2}A}
2sin
2
A
2sinAcosA
After cancellation, we get
= \frac{cosA}{sinA}
sinA
cosA
= cotAcotA
= RHSRHS
Therefore,
\frac{sin2A}{1-cos2A}
1−cos2A
sin2A
=cotA
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