Additional Maths question help!

I was wondering if anyone has any ideas how to answer this question?

Any help would be great :smile:

. Use the given triangle ( image of right angled triangle with sides labelled a,b,c and one angle labelled theta)

to prove that for 0<(theta) <90
1+tan squared theta = 1 over cos squared theta

Reply 1

nuodai

It's probably easier to prove that

\sin^2 \theta + \cos^2 \equiv 1

first, and then just divide through by

\cos^2 \theta

. Say that the hypotenuse has length 1, and then use SOH-CAH-TOA (to find the lengths of the other two sides in terms of

\theta

) and then Pythagoras's theorem (to get the required equation).

(edited 13 years ago)

Reply 2

jameswhughes

Use pythagoras to show sin^2 (theta) + cos^2 (theta)=1, then divide through by cos^2 theta to get the next equation.

Reply 3

sohail.s

Original post by KellyLouiseee

I was wondering if anyone has any ideas how to answer this question?

Any help would be great :smile:

. Use the given triangle ( image of right angled triangle with sides labelled a,b,c and one angle labelled theta)

to prove that for 0<(theta) <90
1+tan squared theta = 1 over cos squared theta

not sure if this is cheating but im assuming you still get taught the basic trig identity that sin^2x + cos^2x = 1
divide both sides by cos^x

you'll get 1 + tan^2x = 1/cos^2x (known as sec^2x)

Reply 4

insparato

c^2 = a^2 + b^2

and tan theta = b/a and cos theta = c/a That is in my head c - hypo, b - opp, and a - adj

See if that nudges you in the right direction.