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Question

If sec4A=cosecA-20°, where 4A is an acute angle, find the value of A.


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Solution

Find the required value.

An angle that is less than 90° is called an acute angle.

Since, 4A is an acute angle.

Therefore, 4A<90°

A<22.5°

Write sec(4A) in terms of cosecant as follows:

sec(4A)=cosec(90°-4A)...1

Also, sec4A=cosecA-20°...2 {Given}

Compare equation 1 and equation 2.

A-20°=90°-4A5A=110°A=22°

Which also satisfies A<22.5°.

Hence, the value of A is 22°.


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