If θ is an acute angle and \tan^2\theta+ 1/\tan ^2\theta = 2, then the value of θ is

RRB NTPC Prelims Model Paper 2 with solutions

Question : 48 of 101

Marks: +1, -0

If θ is an acute angle and

tan^2θ+ 1/tan ^2θ = 2

, then the value of θ is

Solution:

tan^2θ + 1//*{tan^2 θ}*/= 2

{tan^4 θ+ 1}/{tan ^2θ}= 2

⇒ tan^4θ +1 = 2tan^2θ

tan^4θ - 2tan^2θ +1 =0

⇒ ( tan^2θ -1 )^2 = 0

⇒ tan^2θ -1 = 0

⇒ tan^2θ = 1

⇒ tanθ = 1

⇒ θ= 45°

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