Question

prove that cot 2a + tan a = cosec 2a​

Answer 1

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To prove -

cot2a + tana = Cosec 2a .

Proof -

Taking LHS →

→cot 2a + tan a

Convert cot and tan in terms of sine and cosine.

$\frac{ \cos(2a) }{ \sin(2a) } + \frac{ \sin(a) }{ \cos(a) }$

Taking sin2a.cosa as LCM

$\frac{ \cos(2a). \cos(a) + \sin(2a. \sin(a) ) }{ \sin(2a). \cos(a) }$

Now we know that cos ( A-B) = cosAcosB+sinAsinB.So ,

$\frac{ \cos(2a - a) }{ \sin(2a). \cos(a) }$

$\frac{ \cos(a) }{ \sin(2a). \cos(a) }$

$\frac{1}{ \sin(2a) }$

We know that reciprocal of sine is Cosec,

→ LHS = Cosec2a = RHS

hence proved