If sec 4 A =operatorname{cosec}( A -20), where 4 A is a measure of acute angle then value of A is ld

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8. Introduction to Trigonometry

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If $\sec 4 A =\operatorname{cosec}( A -20),$ where $4 A$ is a measure of acute angle then the value of $A$ is $\ldots \ldots \ldots \ldots .$

A

$45$

B

$70$

C

$30$

D

$22$

Solution

$\sec 4 A =\operatorname{cosec}( A -20)$

$\therefore \operatorname{cosec}(90-4 A )=\operatorname{cosec}( A -20)$

$\therefore 90-4 A = A -2 O$

$\therefore 90+20=A+4 A$

$\therefore 5 A=110$

$\therefore A=22$

Standard 10

Mathematics

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