Q16 of 48 Page 86

If sec 5θ = cosec (θ – 36°) where 5θ is an acute angle then find the value of θ.

As we know,


cosec θ = sec (90˚ – θ)


⇒ sec 5θ = sec (90˚ – (θ – 36˚))


⇒ sec 5θ = sec (90˚ – θ + 36˚)


⇒ sec 5θ = sec (126˚ – θ)


Since, 5θ ia an acute angle.


⇒ 5θ = 126˚ – θ


⇒ 6θ = 126˚


⇒ θ = = 21˚


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