Question

IF
$\sin( a) + \cos(a) = \sqrt{2} \: then \: find \: \tan(a) + \: \cot( a)$

Answer 1

The answer is given below :

We consider : θ = α.

Now,

$sin \alpha + cos \alpha = \sqrt{2} \\ \\ or \: \: \frac{1}{ \sqrt{2} } sin \alpha + \frac{1}{ \sqrt{2} } cos \alpha = 1 \\ \\ or \: \: cos45 \: sin \alpha + sin45 \: cos \alpha = 1 \\ \\ or \: \: sin(45 + \alpha ) = sin90 \\ \\ or \: \: 45 + \alpha = 90 \\ \\ or \: \: \alpha = 45$

Now,

$tan \alpha + cot \alpha \\ \\ = tan45 + cot45 \\ \\ = 1 + 1 \\ \\ = 2$

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