Question

prove that:-

tan x +cot x = 2cosec 2x

and deduce (help) that tan75°+cot75°=4


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Answer 1

SOLUTION

$= > tanx + cotx = \frac{sinx}{cosx} + \frac{cosx}{sinx} \\ \\ = > \frac{sin {}^{2}x + {cos}^{2} x }{sinx \: cosx} \\ \\ = > \frac{1}{sinx \: cosx} \\ \\ = > \frac{2}{2sinx \: cosx} \\ \\ = > \frac{2}{2sin(2x)} \\ \\ = > 2cosec(2x)$

hope it helps ✔️

Answer 2

Answer

:hello mate..

here is your answer..

tanx + cotx = sinx / cosx + cosx / sinx

= [sin2x + cos2x] / (sinxcosx)

= 1 / (sinxcosx) = 2 / (2sinxcosx) = 2 / sin(2x)

= 2csc(2x)

So, tan75° + cot75° = 2csc150°

= 2(1 / sin150°) = 2(1 / (1/2)) = 4 ...

i hope it will help you....

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