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Question

When 0<θ<90, Solve the following equations :
(i) 2cos2θ+sinθ2=0
(ii) 3cosθ=2sin2θ
(iii)sec2θ2tanθ=0
(iv)tan2θ=3(secθ1).

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Solution

A) 2cos2θ+sinθ2=0
or, 22sin2θ+sinθ20
or, sinθ(2sinθ+1)=0
Since θ0, sinθ=12θ=30o. [Since 0o<θ<90o]

B) 3cosθ=2sin2θ
or, 3cosθ=22cos2θ
or, 2cos2θ3cosθ2=0
or, (2cosθ1)(cosθ+2)=0
Since cosθ2, cosθ=12θ=60o [Since 0o<θ<90o]

C) sec2θ2tanθ=0
or, 1+tan2θ2tanθ=0
or, (tanθ1)2=0
tanθ=1θ=45o[Since 0o<θ<90o]

D) tan2θ=3(secθ1)
or, sec2θ1=3(secθ1)
or, sec2θ3secθ+2=0
or, (secθ1)(secθ2)=0
Since 0o<θ<90o, secθ=2θ=600.

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