Question

sec⁻¹(cosec(π/8)), Evaluate it.

Answer 1

answer : 3π/8

explanation : we have to find out value of sec⁻¹(cosec(π/8)).

we know, sec(π/2 - θ) = cosecθ

so, cosec(π/8) = sec(π/2 - π/8) = sec(6π/16) = sec(3π/8)

hence, cosec(π/8) = sec(3π/8)

now sec⁻¹(cosec(π/8)) = sec⁻¹(sec(3π/8))

we know from inverse trigonometric formula

sec⁻¹(sec x) = x , when x $\in$ [0, π] -{π/2}

here, (3π/8) lies between [0, π] and 3π/8 ≠ π/2

so, sec⁻¹(sec(3π/8)) = 3π/8

also read :

cos⁻¹(sin π/7), Evaluate it.

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