If \tan \theta+\cot\theta=x, then what is the value of \tan^4 \theta+ \cot^4\theta?

Correct Answer is : x2(x2−4)+2

SSC CGL Model Paper 14

Question : 70 of 100

Marks: +1, -0

\tan θ+\cotθ=x,

then what is the value of

\tan^4 θ+ \cot^4θ

Solution:

\tan θ+\cotθ=x

On squaring both sides,

\tan^2θ+\cot^2θ+2\tanθ\cotθ=x^2

\tan^2θ+\cot^2θ +2=x^2

\tan^2θ+\cot^2θ =x^2-2

On squaring both sides,

\tan^4θ+\cot^4θ+2\tan^2θ\cot^2θ

=x^4+4-4x^2

\tan^4θ+\cot^4θ

=x^4 -4x^2+4-2

=x^2(x^2-4)+2

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