Question

solve it question ..urgent...~​

Answer 1

refer to pic above plz ...

Answer 2

Answer :

prove that,tan⁻¹(1/2) = π/4 - 1/2cos⁻¹(4/5)

cos⁻¹(4/5) = Ф 

cosФ = 4/5 

(1 - tan²Ф/2)/(1 + tan²Ф/2) = 4/5 

5 - 5tan²Ф/2 = 4 + 4tan²Ф/2

tan²Ф/2 = 1/9 = 1/(3)²

tanФ/2 = 1/3 

means, we have to prove, 1/2 = tan[π/4 - Ф/2]

RHS = tan[π/4 - Ф/2]

= {tanπ/4 - tan(Ф/2)}/{1 + tanπ/4.tan(Ф/2)}

= { 1 - tanФ/2 }/{1 + tanФ/2} 

= {1 - 1/3}/{1 + 1/3} 

= {3 - 1}/{3 + 1}

= 2/4 = 1/2 = LHS 

$\rule{200}{2}$