Trigonometric Equations (1 Viewer)

[FDownes]

I'm not sure how to tackle this question, can anyone help me out? It asks;

a) Show that (1 - cos2x)/(1 + cos2x) = tan²x.

b) Hence find the value of tan 22.5^o in simplest exact form.

 

[midifile]

I'm not sure how to tackle this question, can anyone help me out? It asks;

a) Show that (1 - cos2x)/(1 + cos2x) = tan²x.

b) Hence find the value of tan 22.5^o in simplest exact form.

a) (1 - cos2x)/(1 + cos2x) = ((1-(1-2sin²x))/(1+(2cos²x-1))
=2sin²x/2cos²x
=tan²x

b) therefore tan²22.5 = (1-cos45)/(1+cos45)
= (1-(1/sqrt2))/(1+(1/sqrt2)
=(sqrt2-1)/(sqrt2+1)
therefore tan22.5=sqrt((sqrt2-1)/(sqrt2+1))

 

[lolokay]

b) 1-cos45/1+cos45
= (1-1/rt2)/(1+1/rt2) * rt2/rt2 * (rt2 - 1)/(rt2 - 1)
= (rt2 - 1)²/(2-1)
tan²22.5 = (rt2 - 1)²
hence tan22.5 = rt2 - 1

 

[midifile]

b) 1-cos45/1+cos45
= (1-1/rt2)/(1+1/rt2) * rt2/rt2 * (rt2 - 1)/(rt2 - 1)
= (rt2 - 1)²/(2-1)
tan²22.5 = (rt2 - 1)²
hence tan22.5 = rt2 - 1

Oops. I didnt see the word "simplest".

 

[bored of sc]

This question was in our test.

Too bad I forgot the formula said tan²x . There goes a mark.