If sec 4 A =operatorname{cosec}left( A -20^{circ}right), where 4 A is an acute angle, value of A . (

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8. Introduction to Trigonometry

easy

If $\sec 4 A =\operatorname{cosec}\left( A -20^{\circ}\right),$ where $4 A$ is an acute angle, find the value of $A$. (in $^{\circ}$)

A

$110$

B

$22$

C

$50$

D

$90$

Solution

Given that,

$\sec 4 A =\operatorname{cosec}\left( A -20^{\circ}\right)$

$\operatorname{cosec}\left(90^{\circ}-4 A \right)=\operatorname{cosec}\left( A -20^{\circ}\right)$

$90^{\circ}-4 A = A -20^{\circ}$

$110^{\circ}=5 A$

$A=22^{\circ}$

Standard 10

Mathematics

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