Question

Prove cos^2 t+4cos t+4/cos t+2=2sec t+1/sec t

Answer 1

`\text{L.H.S}\\\\=(\cos^2 t +4\cos t +4)/(\cos t +2 )\\\\\\=((\cos t)^2 + 2\cdot 2\cos t+2^2)/(\cos t +2)\\\\\\=((\cos t +2)^2 )/(\cos t +2)\\\\\\=\cos t +2\\\\\\=\frac 1{\sec t} +2\\\\\\=(2\sec t +1)/(\sec t)\\\\\\=\text{R.H.S}\\\\\text{Proved.}`