Sin 163 degrees sin223 degrees +sin253 degrees sin3 13 degrees.

=sin 17 degree sine (-43 degrees)+sine (-73 degrees) sine (-47 degrees)

=-sin 17 degrees sin43 degrees +sin73 degrees sin47 degrees.

=-sin 17 degrees sin43 degrees +cos 17 degrees cos43 degrees.

=cos( 17 degrees +43 degrees)

=cos60 degrees

= 1/2

2.

y=sin^4(x)+cos^2(x)

=[sin^2(x)]^2+[ 1-sin^2(x)]

={[sin^2(x)]^2-sin^2(x)}+ 1

={sin^2(x)[sin^2(x)- 1]}+ 1

={sin^2(x)[-cos^2(x)]}+ 1

=-(sinxcosx)^2+ 1

=-( 1/4)(2sinxcosx)^2+ 1

=-( 1/4)(sin2x)^2+ 1

=-( 1/4)*[( 1-cos4x)/2]+ 1

=( 1/8)cos4x+(7/8)

Then:

Minimum positive period =2π/4=π/2

3.

( 1)

[sin 7+cos 15 sin 8]/[cos 7-sin 15 sin 8]

=[sin( 15-8)+cos 15 sin 8]/[cos( 15-8)-sin 15 sin 8]

=[(sin 15 cos 8-sin 8 cos 15)+cos 15 sin 8]/[(cos 15 cos 8+sin 15 sin 8)-sin 15 sin 8]

=[sin 15 cos 8]/[cos 15 cos 8]

=[sin 15]/[cos 15]

=2-√3

(2)

(2cos 10-sin20)/cos20

=(2cos 10-cos70)/cos20

=[cos 10+(cos 10-cos 70)]/cos 20

=[cos 10+2 sin 40 * sin 30]/cos 20

=[cos 10+2 *( 1/2)* sin 40]/cos 20

=[cos 10+sin40]/cos20

=[cos 10+cos50]/cos20

=[2cos30*cos20]/cos20

=2cos30

= root number 3