If \tan^2\theta+\cot^2\theta=x what is the value of \sec\theta\cosec\theta?

Trigonometry Practice Test 1

Question : 8 of 40

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\tan^2θ+\cot^2θ=x

what is the value of

\secθ\cosecθ?

Solution:

\tan^2θ+\cot^2θ=x

⇒\sec^2θ-1+\cosec^2θ-1=x

⇒1/{\cos^2θ}+1/{\sin^2θ}=x+2

⇒{\sin^2θ+\cos^2θ}/{\sin^2θ\cos^2θ}=x+2

⇒\sec^2θ\cosec^2θ=x+2

⇒\sec θ\cosec θ=√{x+2}

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