Question

prove that cot theta +tan theta =cosec theta×sec theta

Answer 1

In R. H. S
cot A+tan A
we can write this as cos A ÷ sin A +sin A ÷ cosA
so,
cosA²+sinA²÷sinA*×cosA
cos A²+sinA²=1
1÷sinA×cosA
now,
1÷sinA×1÷cosA
cosecA × secA
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Answer 2

To prove:

$cot \theta +tan \theta =cosec \theta \times sec \theta$

Answer:

$cot\theta + tan\theta = cosec \theta \times sec \theta$

LHS is

$Cot \theta + tan \theta= \frac {cos \theta }{sin \theta }+ \frac {sin \theta }{ cos \theta }$

$= \frac {cos^{2} \theta + sin^{2} \theta}{ sin \theta \times cos \theta}$      

Therefore $cos^{2} \theta + sin^{2} \theta = 1$

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

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

Therefore,

$cot \theta +tan \theta =cosec \theta \times sec \theta$

Hence proved.