IF a ,b ,c ARE IN AP ,THEN * 1. 2b=a+c 2. b=a+c, 3. b=ac, 4. c=ab
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4sin50° - √3tan50°
= 4sin50° - √3sin50°/cos50°
= ( 4sin50.cos50° - √3sin50°)/cos50°
use formula ,
2sinAcosA = sin2A
= { 2sin100° - √3sin50° }/cos50°
= 2{ sin(180°-80°) - √3/2 sin50°}/cos50°
= 2{ sin80° - cos30°.sin50°}cos50°
= 2{ sin80° -1/2(2sin50°.cos30°)}cos50°
use formula ,
2sinA.cosB = sin( A+B)+sin(A - B)
= 2{ sin80° -1/2( sin80° + sin20°)}/cos50°
= 2{ 1/2sin80° - 1/2sin20°}/cos50°
= ( sin80° - sin20°)/cos50°
use formula ,
sinA - sinB = 2cos( A + B)/2.sin(A - B)/2
={2cos( 80+20)/2.sin(80-20)/2 }/cos50°
= 2cos50° .sin30°/cos50°
= 2sin30°
= 2 × 1/2 = 1
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