Question

find the value of √3 *cosec 20 - sec 20 .

Answer 1

√3cosec20°-sec20°

=√3/sin20°-1/cos20°

=(√3cos20°-sin20°)/(sin20°.cos20°)

=2{(√3/2)cos20°-(1/2)sin20°}/1/2(2sin20°.cos20°)

=4{sin60°.cos20°-cos60°sin20°}/(2sin20°.cos20°)

use formula
2sinA.cosA=sin2A
and ,
sinA.cosB-cosA.sinB=sin(A-B)

hence,
=4sin(60°-20°)/(sin40°)

=4sin40°/sin40°=4

Answer 2

√3cosec20°-sec20°

=√3/sin20°-1/cos20°

=(√3cos20°-sin20°)/(sin20°.cos20°)

=2{(√3/2)cos20°-(1/2)sin20°}/1/2(2sin20°.cos20°)

=4{sin60°.cos20°-cos60°sin20°}/(2sin20°.cos20°)

use formula
2sinA.cosA=sin2A
and ,
sinA.cosB-cosA.sinB=sin(A-B)

hence,
=4sin(60°-20°)/(sin40°)

=4sin40°/sin40°=4