Question

I need help on this it’s about trig identities

Answer 1

Answer:

The answer to your question is:

Step-by-step explanation:

1.-

$\frac{1 + sin\alpha }{cos\alpha } + \frac{cos\alpha }{1 + sin\alpha } = 2 sec\alpha$

$\frac{(1 + sin\alpha)^{2} + cos^{2} \alpha }{cos\alpha (1 + sin\alpha) }$

$\frac{1 + 2sin\alpha + sin^{2} \alpha+ cos^{2} \alpha }{cos\alpha + sin\alphacos\alpha }$

$\frac{2 + 2sin\alpha }{cos\alpha+ sin\alpha cos\alpha }$

$\frac{2(1 + sin\alpha) }{cos\alpha(1 + sin\alpha ) }$

$\frac{2}{cos\alpha }$

2sec$\alpha$

2.-

   sec²x - tanxsecx

$\frac{1}{cos^{2}x } - \frac{sinx}{cosx} \frac{1}{cosx}$

$\frac{1}{cos^{2} x} - \frac{sinx}{cos^{2}x}$

$\frac{1 - sinx}{cos^{2}x }$

$\frac{1 - sinx}{1 - sin^{2}x }$

$\frac{1 - sinx}{(1 - sinx)(1 + sinx)}$

$\frac{1}{1 + sinx}$