Question

IF a ,b ,c ARE IN AP ,THEN * 1. 2b=a+c 2. b=a+c, 3. b=ac, 4. c=ab

Answer 1

Answer:

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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