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Question
If 4 sin2 θ - 1= 0 and angle θ is less than 90°, find the value of θ and hence the value of cos2 θ + tan2θ.
Solution
4 sin2 θ – 1 = 0
sin2 θ = `(1)/(4)`
sin θ = `(1)/(2)`
sin θ = sin30°
θ = 30°
cos2 θ + tan2 θ= cos230° + tan230°
= `(sqrt3/2)^2 + ( 1/sqrt3)^2`
= `(3)/(4) + (1)/(3)`
= `(9 + 4)/(12)`
= `(13)/(12)`
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