CLASS-10
TRIGONOMETRY - QUOTIENT RELATIONS
Quotient Relations –
Theorem 2. For an acute angle A, prove that
sin A cos A
(i) --------- = tan A, (ii) --------- = cot A, (iii) tan A. cot A = 1
cos A sin A
Proof; we have -
BC AB
sin A = --------, and cos A = --------
AC AC
sin A BC / AC BC AC
(i) --------- = ---------- = (------ X ------)
cos A AB / AC AC AB
BC
= -------- = tan A (Proved)
AB
cos A AB / AC AB AC
(ii) --------- = ----------- = (------- X --------)
sin A BC / AC AC BC
AB
= ------ = cot A (Proved)
BC
BC AB
(iii) tan A . cot A = --------- X -------- = 1 (Proved)
AB BC
Your second block of text...