Question

CotA-tan A=2 Cot 2A​

Answer 1

Step-by-step explanation:

$\cot(a ) - \tan(a)$

cos÷sin-sin÷cos

=cos*2-sin*2÷sin.cos

=cos2a÷sina.cosa

=2cos2a÷2sina.cosa

=2cos2a÷sin2a=2cot2a

Answer 2

${\mathcal{\red{ANSWER}}}$

$\tt{LHS = cot\;A-tan\;A}$

$\tt{\implies \dfrac{cos\;A}{sin\;A}-\dfrac{sin\;A}{cos\;A}}$

$\tt{\implies \dfrac{cos^{2}\;A-sin^{2}\;A}{sin\;A.cos\;A}}$

$\tt{\implies \dfrac{cos\;2A}{sin\;A.cos\;A}}$

$\tt{\implies \dfrac{2\;cos\;2A}{2\;sin\;A.cos\;A}}$

$\tt{\implies \dfrac{2\;cos\;2A}{sin\;2A}}$

$\tt{\implies 2\;cot\;2A}$

$\tt{=RHS}$

Hence Proved!!