Question

If t is any real number, prove that 1+(tant)^2=(sect)^2

Answer 1

`1+\left(tant\right)^2=\left(sect\right)^2\\\\L=1+\left((sint)/(cost)\right)^2=1+(sin^2t)/(cos^2t)=(cos^2t)/(cos^2t)+(sin^2t)/(cos^2t)=(cos^2t+sin^2)/(cos^2t)=(1)/(cos^2t)\\\\=\left((1)/(cost)\right)^2=(sect)^2=R\\\\====================================\\\\\\tanx=(sinx)/(cosx)\\\\sin^2x+cos^2x=1\\\\secx=(1)/(cosx)`