abcd is a quadilateral prove that cos a+b / 4 = sin c+d /4

Asked by harishankarpandabrl | 9th Jul, 2020, 03:37: PM

Expert Answer:

Given: abcd is quadrilateral
We need to prove:- cos[(a+b)/4] = sin[(c+d)/4]
A s space a b c d space i s space a space q u a d r i l a t e r a l comma space w e space h a v e
angle a plus angle b plus angle c plus angle d equals 360 degree
rightwards double arrow angle a plus angle b equals 360 degree minus angle c minus angle d
rightwards double arrow fraction numerator angle a plus angle b over denominator 4 end fraction equals 90 degree minus fraction numerator angle c plus angle d over denominator 4 end fraction
rightwards double arrow cos open parentheses fraction numerator angle a plus angle b over denominator 4 end fraction close parentheses equals cos open parentheses 90 degree minus fraction numerator angle c plus angle d over denominator 4 end fraction close parentheses
rightwards double arrow cos open parentheses fraction numerator angle a plus angle b over denominator 4 end fraction close parentheses equals sin open parentheses fraction numerator angle c plus angle d over denominator 4 end fraction close parentheses space... space S i n c e space cos left parenthesis 90 degree minus x right parenthesis equals sin x

Answered by Renu Varma | 10th Jul, 2020, 09:11: AM