Question

prove the identity 1-cos 2α/sin 2α = tanα

Answer 1

Answer: 1-cos2a/sin2a=tan a

LHS

=(1-(cos^2a-sin^2a))/2sinacosa

=(sin^2a+cos^2a-cos^2a+sin^2a)/2sinacosa

=2sin^2a/2sinacosa

=sina/cosa

=tan a

=RHS (Proved)

Step-by-step explanation:

Answer 2

$cos \: 2a \: = 1 - 2{sin }^{2} a$

$sin \: 2a = 2(sin \: a)(cos \: a)$

putting valued

$\frac{1 - (1 - 2{sin }^{2}a)}{2(sin \: a)(cos \: a)}$

$\frac{2 \: sina.sina}{2 \: sina.cosa}$

$\frac{sin \: a}{cos \: a}$

$tan \: a$

hence proved

Hope it helps!!!