Question

If Sin a+cos a =root2 then prove tan a+cot a=2

Answer 1

Answer:

i don't no it is correct or not

Answer 2

Answer:

$( \sin( \alpha ) + \cos( \alpha )) {}^{2} = 2$

$\sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) + 2 \sin( \alpha ) \cos( \alpha ) = 2$

$1 + \sin(2 \alpha ) = 2$

$\sin(2 \alpha ) = 1 = \sin( \frac{\pi}{2} )$

$2 \alpha = \frac{\pi}{2} \:$

$\alpha = \frac{\pi}{4}$

Now from LHS,

$\tan( \frac{\pi}{4} ) + \cot( \frac{\pi}{4} ) = 1 + 1 = 2$

proved.

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