Question

verify sinx+cosxcotx=cscx

Answer 1

can you write cotx in terms of sine and cosine?

cotx = ???

Answer 2

1/tanx

Answer 3

... in terms of sine and cosine...

Answer 4

oh cosx/sinx

Answer 5

ok... good... so...

Answer 6

\(\large sinx+cosxcotx \)
= \(\large sinx+cosx \frac{cosx}{sinx} \)
= \(\large sinx+\frac{cos^2x}{sinx} \)

now, in order to add these two, they must have the same denominator... what is it?

Answer 7

= \(\large sinx+\frac{cos^2x}{sinx} \)
= \(\large \frac{sinx}{1}+\frac{cos^2x}{sinx} \)

they must have the common denominator of sinx.... agreed?

Answer 8

o sorry yeah

Answer 9

so...
= \(\large \frac{sinx}{1}+\frac{cos^2x}{sinx} \)
= \(\large \frac{sinx}{sinx} \cdot \frac{sinx}{1}+\frac{cos^2x}{sinx} \)
= \(\large \frac{sin^2x}{sinx}+\frac{cos^2x}{sinx} \)
= \(\large \frac{sin^2x + cos^2x}{sinx} \)
= i think you can take it from here?

Answer 10

yes thank you