Question

If (tan $\theta$ + cot $\theta$) = 5 then ($ta{n}^2\theta$ + $co{t}^2\theta$) = ?

(a) 27 (b) 25 (c) 24 (d) 23

Answer 1

(tan $\theta$ + cot $\theta$) = 5 (given)

$(tan\theta +cot\theta {)}^2=(5{)}^2$(squaring both sides)

$ta{n}^2\theta +co{t}^2\theta +2\times tan\theta \times cot\theta =25$

$[\because (a+b{)}^2=a^2+b^2+2ab]$

$ta{n}^2\theta +co{t}^2\theta +2\times 1=25$

$\because tan\theta \times cot\theta =tan\theta \times \frac{1}{tan\theta }=1)$

$ta{n}^2\theta +co{t}^2\theta =25-2=23$