3. Evaluate:
(i) (sin263° + sin227°)/(cos217° + cos273°)
(ii) sin 25° cos 65° + cos 25° sin 65°
Answers
(i) (sin263° + sin227°)/(cos217° + cos273°)
To simplify this, convert some of the sin functions into cos functions and cos function into sin function and it becomes,
= [sin2(90°-27°) + sin227°] / [cos2(90°-73°) + cos273°)]
= (cos227° + sin227°)/(sin227° + cos273°)
= 1/1 =1 (since sin2A + cos2A = 1)
Therefore, (sin263° + sin227°)/(cos217° + cos273°) = 1
(ii) sin 25° cos 65° + cos 25° sin 65°
To simplify this, convert some of the sin functions into cos functions and cos function into sin function and it becomes,
= sin(90°-25°) cos 65° + cos (90°-65°) sin 65°
= cos 65° cos 65° + sin 65° sin 65°
= cos265° + sin265° = 1 (since sin2A + cos2A = 1)
Therefore, sin 25° cos 65° + cos 25° sin 65° = 1
Answer:
(i) (sin263° + sin227°)/(cos217° + cos273°)
To simplify this, convert some of the sin functions into cos functions and cos function into sin function and it becomes,
= [sin2(90°-27°) + sin227°] / [cos2(90°-73°) + cos273°)]
= (cos227° + sin227°)/(sin227° + cos273°)
= 1/1 =1 (since sin2A + cos2A = 1)
Therefore, (sin263° + sin227°)/(cos217° + cos273°) = 1
(ii) sin 25° cos 65° + cos 25° sin 65°
To simplify this, convert some of the sin functions into cos functions and cos function into sin function and it becomes,
= sin(90°-25°) cos 65° + cos (90°-65°) sin 65°
= cos 65° cos 65° + sin 65° sin 65°
= cos265° + sin265° = 1 (since sin2A + cos2A = 1)
Therefore, sin 25° cos 65° + cos 25° sin 65° = 1