Question

find tan 75 - cot 75..

Answer 1

Answer:

$Value \:of\:\\ tan75\degree -cot75\degree =2\sqrt{3}$

Step-by-step explanation:

$Value \:of\: tan75\degree -cot75\degree$

=$\frac{sin75}{cos75}-\frac{cos75}{sin75}$

=$\frac{(sin^{2}75-cos^{2}75)}{(cos75sin75)}$

=$\frac{-(cos^{2}75-sin^{2}75}{\frac{1}{2}\times 2\times sin75cos75}$

/* we know that,

i ) cos²A - sin²A = cos2A

ii ) 2sinAcosA = sin2A */

=$\frac{-2cos(2\times 75)}{sin(2 \times 75)}$

= $\frac{-2cos(150)}{sin(150)}$

= $-2cot150$

= $-2cot(90+60)$

= $-2\times (-tan60)$

= $2tan60$

=$ 2\times \sqrt{3}$

=$2\sqrt{3}$

Therefore,.

$Value \:of\:\\ tan75\degree -cot75\degree =2\sqrt{3}$

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Answer 2

Answer:

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