Question

Verify the identity. (1 - sinx)/cosx = cosx/(1 + sinx)

Answer 1

hi @IBhardcore :)

for your identity, what you can do as a first step is
multiply and divide by 1+sin x
\(\large \dfrac{1-\sin x}{\cos x} \: \dfrac{1+\sin x}{1+\sin x}\)
now can you simplify the numerator ?

Answer 2

sin ^2x + 1?

Answer 3

you sure ?
hint : \((a+b)(a-b) = a^2-b^2 \\ (1-\sin x )(1+\sin x)=...?\)

Answer 4

1 - sin^2x

Answer 5

correct!
and using
\(\sin^2 x+\cos^2 x =1\)
what does
1 - sin^2x simplify to ???

Answer 6

cos^2x

Answer 7

good!
now numerator has cos^2 x = cos x * cos x
denominator has cos x (1+ sin x)
notice that one cos x gets cancelled!
what remains ?

Answer 8

cos x / 1+ sin x !

Answer 9

good! you got it :)

Answer 10

Thanks!! :)

Answer 11

welcome ^_^