Question

if X = 1+ sin A/ cosA then prove that 1/X = 1 - sinA/ cosA​

Answer 1

Answer:

X=1+sinA/cosA

Rationalizing it

X=(1+sinA)(1-sinA)/cosA (1-sinA)

X=(1-sin^A)/cosA (1-sinA)

:( (a+b)(a-b)= a^2-b^2)

X=cos^2A /cosA (1-sinA)

: (1-sin^2A=cos^2A)

X=cosA/1-sinA

Now taking reciprocal

1/X=1-sinA/cosA