CLASS-10
TRIGONOMETRY - RELATION BETWEEN TRIGONOMETRICAL-RATIOS
Relation Between T-Ratios -
Theorem 1. For an acute angle A (Please Note – Sometimes instead of A, we take the angle as Theta ‘θ’), prove that –
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(i) cosec A = --------, (ii) sec A = --------, (iii) cot A = --------
sin A cos A tan A
Proof - We have,
AC BC
(i) cosec A = --------, and sin A = -------
BC AC
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So, cosec A = ----------- = --------
BC / AC sin A
AC AB
(ii) sec A = --------, and cos A = ---------
AB AC
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So, sec A = ----------- = --------
AB / AC cos A
AB BC
(iii) cot A = ---------, and tan A = -------
BC AB
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So, cot A = ---------- = ---------
BC / AB tan A
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