Question

If tan theta + cot theta =5, then find tan square theta + cot square theta

Answer 1

$if \: \tan\theta + \cot\theta= 5$

→ To find

$\tan ^{2}\theta + cot ^{2}\theta$

✓ Solution :

$\tan\theta + \cot\theta= 5$

By squaring on both the sides ,

${( tan\theta+\cot\theta)^{2}} = 25$

$\longrightarrow {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

${tan}^{2}\theta+{cot}^{2}\theta+2 \times \tan\theta\times\cot\theta = 25$

Since cot\theta= 1/tan\theta

2tan\theta* (1/tan\theta) = 2

Let's write the remaining part

${tan}^{2}\theta+ {cot}^{2}\theta = 25 - 2$

${tan}^{2}\theta+{cot}^{2}\theta= 23$

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