1.Evaluate the following using half angle identities
(a) tan (75◦)
(b) cos (120◦)
2. Evaluate cos (195◦) + cos (105◦) using sum-to-product/difference-to-product identities.
Answers
2. cos 195+cos 105=2cos(195+105)/2*(cos)195-95)/2
=2cos(300/2)*cos(90/2)
=2cos(150)*cos(45)
=2*-root 3/2* root 2/2
= -root 6/2=-1.224
1.(a) tan75=tan 150/2=1-cos 150/sin 150^2
=1-cos150/sin 150
=1+cos30/sin30
=1+root3/2(root just over 3)/1/2 (this whole thing is divided by 1/2)
=2+root 3
(b) cos 120=cos(240/2)=-whole root 1+cos 240 / 2(whole thing divided by 2) [CAN I GET DETAILED WORKINGS FOR THIS MATH?]
= -1/2
(a) tan (75◦)
(b) cos (120◦)
2. Evaluate cos (195◦) + cos (105◦) using sum-to-product/difference-to-product identities.
Answers
2. cos 195+cos 105=2cos(195+105)/2*(cos)195-95)/2
=2cos(300/2)*cos(90/2)
=2cos(150)*cos(45)
=2*-root 3/2* root 2/2
= -root 6/2=-1.224
1.(a) tan75=tan 150/2=1-cos 150/sin 150^2
=1-cos150/sin 150
=1+cos30/sin30
=1+root3/2(root just over 3)/1/2 (this whole thing is divided by 1/2)
=2+root 3
(b) cos 120=cos(240/2)=-whole root 1+cos 240 / 2(whole thing divided by 2) [CAN I GET DETAILED WORKINGS FOR THIS MATH?]
= -1/2