Question

If sec 4A = cosec (A − 20°), where 4A is an acute angles, find the value of A.

Answer 1

SOLUTION :  

Given : sec 4A = cosec(A − 20°) and 4A  is acute angle.

sec 4A = cosec(A − 20°)

sec 4A = sec{90–(A − 20°)}

[sec (90 - θ) = cosec θ]

sec 4A = sec{90– A + 20°}

sec 4A = sec{110°– A}

On equating both sides,

4A = {110°– A}

4A + A = 110°

5A = 110°

A = 110°/5

A = 22°

Hence, the value of A is 22° .

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Answer 2

sec4A=cosec(A-20)

sec4A=sec20

Comparing both side we got

4A=20

A=20/4

A=5

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