SSC CGL 19 Oct 2014 Shift 2 Paper

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Question : 134 of 200

Marks: +1, -0

If θ is an acute angle and tan θ + cot θ = 2, then the value of

tan^5

θ +

cot^5

θ is

1
2
3
4

Solution:

⇒ tan t +

1/{tanθ}

= 2
⇒

{tan^2t+1}/{tanθ}

= 2
⇒

tan^2

θ +1 = 2 tan θ
⇒

tan^2

θ – 2 tan θ + 1 = 0
⇒

(tan θ –1)^2

= 0
⇒ tan θ – 1= 0 ⇒ tan θ = 1
∴ cot θ =

1/{tanθ}

= 1
∴

tan^5

θ +

cot^5

θ = 1 + 1 = 2

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