Question

Prove that
that √(1-sin ø /1+ Sin ø)
Sec ø - tanø​

Answer 1

Step-by-step explanation:

square root of (1-sinx/1+sinx)

divide and multiply by (1-sinx)

square root of (1-sinx)(1-sinx)/(1+sinx)(1-sinx)

square root of (1-sinx)^2/1-sin^2x

1-sin^2x=cos^2x

square root of (1+sin^2x-2sinx)/cos^2x

square root of (1/cos^2x+sin^2x/cos^2x-2sinx/cos^2x)

=1/cos^2x=sec^2x

=sin^2x/cos^2x=tan^2x

=2sinx/cos^2x=2tanxsecx

square foot of sec^2x+tan^2x-2tanxsecx

it is in the form of (a-b)^2=a^2+b^2-2ab

square root of (secx-tanx)^2

square root and square canceled

therefore secx-tanx

square root of (1-sinx)/(1+sinx)=secx-tanx