Please answer the question no. 13. tan x
12. (i)
1 — cot x
tan x
(ii)
tan2x — 1
tan r
(iii) +
cot r
sec x . cosecx 1
1 — tan x
cosec x
sec x —cosec x sin x —cos x
cof3 r
sec x cosec x — 2 sin x cos x.
I + Cota x
13. If tan' x 1 — k2, show that sec x + tans x cosecx= (2 — k2)V2.
14. If sin x + sin2 x = I; show that COSI x + x = I.
2 sin x.
15. If cos x + sin x = V2 cos x; show that cos x — sin x =
16. If cot x + cosx= m and cot x— cosx = n, prove that (m2 — n2)2 = 16 mn.
3.10. SIGNS OF TRIGONOMETRIC FUNCTIONS
Consider a unit circle with centre at origin O of the coordinate axes. Let
point on the circle such that length of arc AP x or equivalently, let P(a, b)
where the terminal side of LAOP with radian measure x meets the unit circle. '
trigonometric functions of the real number x are defined as
(i) cosx = a, for all x e R
