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Question
If secθ= cosec30° and θ is an acute angle, find the value of 4 sin2θ - 2 cos2θ.
Solution
secθ= cosec30°
⇒ secθ = 2
⇒ secθ = sec60°
⇒ θ = 60°
Now,
4sin2θ - 2cos2θ
= 4sin260° - 2cos260°
= `4 xx (sqrt(3)/2)^2 - 2 xx (1/2)^2`
= `4 xx (3)/(4) - 2 xx (1)/(4)`
= `3 - (1)/(2)`
= `(6 - 1)/(2)`
= `(5)/(2)`.
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