SSC CGL 9 Aug 2015 Shift 2 Paper

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Question : 125 of 200

Marks: +1, -0

If θ is an acute angle and

tan^2

θ +

1/{tan^2 θ}

= 2, then the value of q is :

60°
45°
15°
30°

Solution:

tan^2

θ +

1/{tan^2 θ}

= 2
⇒

{tan^4 θ+1}/{tan^2θ}

= 2
⇒

tan^4θ

+ 1 = 2

tan^2θ

⇒

tan^4θ

– 2

tan^2θ

+ 1 = 0
⇒

( tan^2θ – 1)^2

= 0
⇒

tan^2θ

– 1 = 0
⇒

tan^2θ

= 1
⇒ tan θ = 1 = tan 45°
⇒ q = 45°
Since θ is an acute angle

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