Question

Show
that coto+tano=seco.coseco​

Answer 1

Step-by-step explanation:

tano+coto

=sino/coso+coso/sino

=sin²o+cos²o/sinocoso

=1/sinocoso

=secocoseco

Answer 2

Solution →

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

LHS →

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

$= \frac{cos \: \theta}{sin \: \theta} + \frac{sin \: \theta}{cos \: \theta} \:$

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

We know that →

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

So,

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

We know that →

• $\frac{1}{cos \: \theta} = sec \:\theta$
• $\frac{1}{sin \: \theta} = cosec \:\theta \:$

So,

$\boxed{\purple{= sec \: \theta \times cosec \: \theta}}$RHS

Hence Proved !!

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