यदि एक `DeltaABC,` में, हो` sin A- cosB = cosC` , तो किसके B बराबर है ?

Options

A. `pi`
B. `pi/3`
C. `pi/2`
D. `pi/4`

Answer

c

Explanation

दिया है , ` Delta ABC ` में, ` sin A - cos B = cos C`
` rArr sin A = cosB +cosC`
` rArr 2 sin.= 2 cos. A/2 * cos.A/2 . (B+C)/2* cos. (B-C)/2 `
` rArr sin. A/2 . cos . A/2 = cos (90 - A/2) cos. ((B-C))/2`
` rArr sin . A/2 * cos. A/2 = sin. A/2 * cos. ((B-C))/2`
` rArr cos.A/2 = cos. ((B-C))/2 `
` rArr A/2 = (B-C)/2 rArr A= B-C`
` rArr A+C=B " "` ...(i)
तथा ` A+C = 180^(@) - B " "` ...(ii)
समी (i ) तथा (ii ) से,
` 180^(@) - B=B`
` rArr 2B = 180^(@) rArr B = 90^(@) = pi/2 `