SSC CGL 16 Aug 2015 Shift 2 Paper

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Question : 148 of 200

Marks: +1, -0

If tan A + cot A = 2, then the value of

tan^{10}

A +

cot^{10}

A is

4
2
$2^{10}$
1

Solution:

tanA + cotA = 2
⇒ tanA +

1/{tanA}

= 2
⇒

{tan^2A+1}/{tanA}

= 2
⇒

tan^2

A + 1 = 2 tan A
⇒

tan^2

A - 2 tan A + 1 = 0
⇒

(tanA-1)^2

= 0
⇒ tan A - 1 = 0
⇒ tan A = 1
⇒ cot A = 1
∴

tan^{10}

A +

cot^{10}

A = 1 + 1 = 2

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