Question

15. Prove that:
? cosec? 58°
3
WN
cot 58° tan 32°
Ол
tan 13° tan 37° tan 45º tan 53° tan 77° = -1. [CBSE 2009]
3​

Answer 1

Answer:

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Step-by-step explanation:

$\huge\red{\boxed{\underline{Given:}}}$

==>(tan 13)(tan 37)(tan 45)(tan 53)(tan 77)= -1

Now,

Since, $\large\green{\boxed{Tan \:A * Cot \:A = 1}}$ ------(¡)

Taking LHS:

==>(tan 13)(tan 77)( tan 37)(tan 53)(tan 45)

==>(tan 13)(tan 90 -13)(ran 37)(tan 90 - 37)(tan 45)

==>{(tan 13)(cot 13)}{(tan 37)(cot 37)}(tan 45)

==> 1*1*1

==> 1

Hence, $\large\blue{\boxed{ LHS=RHS}}$

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