Few Trig Q's: prove sec^2(x) = 1 + tan^2(x), etc.

[lesmuse]

Totally stuck on trig, i'm rubbish at it.

1) a)Starting from the identity sin²x + cos²x = 1, prove that sec²x = 1 + tan²x
. . .b) Given that 180 < x < 270 and that tanx° = 7/24, find the exact value of secx°

2) Find in exact form, all the roots of the equation 2sin²x + cosec² = 3 which lie between 0 and 2π.

3) a)State the value of sec²x - tan².
. . .b)The angle A is such that sec A + tan A = 2. Show that sec A - tan A = 1/2,and hence find the exact value of coa A

 

[royhaas]

1) A) Divide by \(\displaystyle cos^2x\).
B) Use the previous identity.
2. First solve for \(\displaystyle sin(x)\).
3)A) Use the identity from first problem.
B) Multiply by \(\displaystyle sec(A)+tan(A)\).