Question

If u =log tan (pi/4 +teta/2) then value of is​

Answer 1

Answer:

sec θ

Step-by-step explanation:

Given  

If y = log tan (pi/4 +  θ/2) then value of  dy/ dθ is

ANSWER

We have

y = log tan(π / 4 + θ/2)

dy / d θ = 1/tan(π/4 +  θ/2) d/d θ [tan(π/4 +  θ/2)] (log x’ = 1/x)

 = cos (π/4 + π/2) / sin (π/4 + π/2) x sec^2(π/4 +  θ/2) x d/dx (π/4 +  θ/2) (since tan  θ’= sec^2  θ )

= cos(π/4 +  θ/2) / sin(π/4 +  θ/2) x 1 / cos^2 (π/4 +  θ/2) x 1/2

 = 1 / 2 sin (π/4 +  θ/2) Cos (π/4 +  θ/2)

= 1 / sin (π/2 +  θ) (since sin 2  θ = 2 sin  θ cos  θ)

= 1/cos θ

= sec θ