Question

prove tan (45+a) = cos2a / 1-sin2a

Answer 1

Answer:Proved

Step-by-step explanation:tan(π/4+a)

tan(a+b)=tan a+tan b/(1-tan a tan b)

tan(π/4+a)=tan π/4+tan a/1-tan π/4 tan a

tan(π/4+a)=1+tan a/1-tan a

tan(π/4+a)=(1+sin a/cosA)/(1-sin a/cos a)

tan(π/4+a)=(cos a+sin a)/(cos a-sin a)

Rationalising, we get

(cos a+sin a)(cos a-sin a)/(cos a-sin a)(cos a-sin a)

cos²a-sin²a/(cos a-sin a)²

cos 2a/(cos²a+2sin a cos a+ sin²a)

Since cos²a+sin²a=1

cos 2a/1-sin 2a

Proved