Question

Prove that :

following

`(tan \: q \: + sec \: q) {}^(2) = (1 + sin \: q \: )/(1 - sin \: q \: )`
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Answer 1

`\text{L.H.S}\\\\=(\tan q + \sec q)^2\\\\\\=\left((\sin q)/( \cos q) + \frac 1{ \cos q} \right)^2\\\\\\=\left( (1+ \sin q)/(\cos q)\right)^2\\\\\\=((1+ \sin q)^2)/(\cos^2 q)\\\\\\=((1+ \sin q)^2)/(1-\sin^2 q)\\\\\\=((1 + \sin q)(1 + \sin q))/((1+ \sin q)(1 - \sin q))\\\\\\=(1+ \sin q)/(1- \sin q)\\\\=\text{R.H.S}\\\\\text{Proved.}`