Question

Trigonometry : Reciprocal relations

Answer 1

sinx=1/cosecx
cosx=1/secx
tanx=1/cotx
cotx=1/tanx
cosecx=1/sinx
secx=1/cosx

Answer 2

Required answer:-

Correct question :

• Explain in trigonometry : Reciprocal relations

Solution :

$1. \: Since, \: sin \: A \: = \: \dfrac{perpendicular}{hypotenuse} \: and \: cosec \: A \: = \: \dfrac{hypotenuse}{perpendicular} \\→ \: sin \: A \: and \: cosec \: A \: are \: reciprocal \: of \: each \: other. \\ ∴ \: sin \: A \: = \: \frac{1}{cosec \: A} \: and \: cosec \: A \: = \: \frac{1}{sinA} \\ Similarly, \: cosA \: = \: \frac{1}{secA} \: \: and \: secA \: = \: \frac{1}{cosA} \\ tan \: A \: = \frac{1}{cot \:A} \: and \: cot \: A \: = \: \frac{1}{tanA}$

$Since, \: \dfrac{sin A}{cosA} \: = \: \frac{ \frac{perpendicular}{hypotenuse} }{ \frac{base}{hypotenuse} } \: = \: \dfrac{perpendicular}{base} \: = \: tan A\: \\ ∴ \: tan \: A \: = \: \frac{sinA}{cosA} \: and \: cot \: A \: = \: \frac{cosA}{sinA}$