Question

prove that Tan 25 =cos 30/sec2teath​

Answer 1

Explanation:

L.H.S. = tan2 θ/(sec θ – 1)2

= (sin2 θ/cos2 θ)/(1/cos θ – 1)    (∵  tan θ = sin θ/cos θ)

= (sin2 θ/cos2 θ)/(1 – cos θ)2/cos2 θ)   (∵ sec θ = 1/cos θ)

= sin2 θ/(1 – cos θ)2     [∵  sin2 θ = 1 – cos2 θ]

= (1 – cos2 θ)/(1 – cos θ)2

= (1 – cos θ)(1 + cos θ)/(1 – cos2 θ)2     {∵ a2 – b2 = (a  + b)(a – b)}

= 1 + cos θ/1 – cos θ