Question

cos theta = n cos (theta + pi) prove ( n+1)tan(theta+pi)=(n-1)cot pi​

Answer 1

Step-by-step explanation:

ANSWER

tan(πcosθ)=tan(2π−πsinθ)

⇒πcosθ=nπ+2π−πsinθ(n∈I)

⇒π(sinθ+cosθ)=(2n+1)2π

⇒sinθ+cosθ=22n+1

⇒cos(4π−θ)=222n+1

Since −1≤cos(4π−θ)≤1

⇒−1≤222n+1≤1

⇒n=0,−1 as n is an integer

⇒cos(4π−θ)=±(221)

⇒8cos2(π/4−θ)=1