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# Help with Life of Fred trig? Page 111

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My son can't figure out how/why a step in the problem at the bottom of page 111 in Life of Fred trigonometry was arrived at. I'm no help, either. Can anyone help?

To show that 1 + cot2 x = csc2 x

Changing to sines and cosines (ok here)              1 + cos2x/sin2x = 1/sin2x

Adding the fractions (this is what he doesn't get)   (sin2x + cos2x)/sin2x

Since sin2x + cos2x = 1 (ok here too)                     1/sin2x

He doesn't understand how the term in the second step is derived.  Anyone?

Thanks!
Amy

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My son can't figure out how/why a step in the problem at the bottom of page 111 in Life of Fred trigonometry was arrived at. I'm no help, either. Can anyone help?

To show that 1 + cot2 x = csc2 x

Changing to sines and cosines (ok here)              1 + cos2x/sin2x = 1/sin2x

Adding the fractions (this is what he doesn't get)   (sin2x + cos2x)/sin2x

Since sin2x + cos2x = 1 (ok here too)                     1/sin2x

He doesn't understand how the term in the second step is derived.  Anyone?

Thanks!

Amy

Two fractions with different denominators must be brought on the common denominator to be added.

1 + cos2x/sin2x

we need to make the 1 into a fraction with the denominator sin2x. So, we multiply top and bottom of 1/1 with sin2x

and get sin2x/sin2x (which is still equal to 1)

Now we can add:

sin2x/sin2x+cos2x/sin2x = add numerators of fractions with like denominators: (sin2x+cos2x)/sin2x

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Thank you so much!!

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