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Introduction to Trigonometry
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16/06/2021 11:20 am
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Evaluate:
\(\frac{1 + sec A}{sec A}\) = \(\frac{sin^2 A}{1-cos A}\)
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16/06/2021 11:22 am
\(\frac{1 + sec A}{sec A}\) = \(\frac{sin^2 A}{1-cos A}\)
L.H.S. = (1 + sec A)/sec A
Since secant function is the inverse function of cos function and it is written as
= (1 + 1/cos A)/1/cos A
= (cos A + 1)/cos A/1/cos A
Therefore, (1 + sec A)/sec A = cos A + 1
R.H.S. = sin2A/(1-cos A)
We know that sin2A = (1 – cos2A), we get
= (1 – cos2A)/(1-cos A)
= (1-cos A)(1+cos A)/(1-cos A)
Therefore, sin2A/(1-cos A)= cos A + 1
L.H.S. = R.H.S.