Question

Prove tan theta + 1 / tan theta = sec theta × cosec theta

Answer 1

hope this will help...

Answer 2

Solution:

LHS = $tan\theta+\frac{1}{tan\theta}$

/* LCM = $tan\theta$*/

= $\frac{(tan^{2}\theta+1)}{tan\theta}$

= $\frac{sec^{2}\theta}{tan\theta}$

/* By Trigonometric identity:*/

$\boxed{1+tan^{2}\theta = sec^{2}\theta}$

= $\frac{\frac{1}{cos^{2}\theta}}{\frac{sin\theta}{cos\theta}}$

= $\frac{1}{sin\theta cos\theta}$

= $\frac{1}{sin\theta}\times\frac{1}{cos\theta}$

= $cosec\theta sec\theta$

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Since ,

i) $\frac{1}{sin\theta} = cosec\theta$

ii)$\frac{1}{cos\theta} = sec\theta$

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= RHS

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