Question

PROVE :(secA+tanA)2 =(1+sinA)/(1/sinA)

Answer 1

`A=x\\\\(secx+tanx)^2=(1+sinx)/(1-sinx)\\\\L=\left((1)/(cosx)+(sinx)/(cosx)\right)^2=\left((1+sinx)/(cosx)\right)^2=((1+sinx)^2)/(cos^2x)\\\\=((1+sinx)^2)/(1-sin^2x)=((1+sinx)^2)/(1^2-sin^2x)=((1+sinx)^2)/((1-sinx)(1+sinx))=(1+sinx)/(1-sinx)=R`



`if\ R=(1+sinx)/((1)/(sinx))=(1+sinx)sinx=sinx+sin^2x\ then\ L\\eq R`



`secx=(1)/(cosx)\\\\tanx=(sinx)/(cosx)\\\\sin^2x+cos^2x=1\to cos^2x=1-sin^2x\\\\a^2-b^2=(a-b)(a+b)`