Chapter1 (Q6) Use identities to find each exact value :a. \(Tan(-7π/12 ) \) b. \(Sin40°cos50°+sin40°sin50° \) c.\ (Tan80°+Tan55°)/(1-Tan80°Tan55°) \)d. \((Tan80°+Tan(-55°))/(1-Tan80°Tan(-55°)\) e.\( (Tan100°+Tan(80°))/(1-Tan100°Tan(80°)\) f. \((Tan 5π/12+Tan π/4)/(1-Tan 5π/12 Tan π/4)\)g. \( Sin π/5 Cos 3π/10 cos π/4+Cos π/5 sin 3π/10 \)

Solution

a.\(Tan(-7π/12)←Tan(π/3+π/4)←-Tan(60°+45°).

Tan (a+b)= (Tana+Tanb)/(1-TanaTanb)←(Tan60°+Tan45°)/(1-Tan60°Tan45°)←(√3+1)/(1-√3 ×1 \))=

b. \( Sin40°cos50°+sin40°sin50°=Sin (40°+50°\))=

c. \((Tan80°+Tan55°)/(1-Tan80°Tan55°)←Tan (a+b)←Tan (80°+55° \))=

d. \((Tan80°+Tan(-55°))/(1-Tan80°Tan(-55°))←Tan (80°-(-55°)←Tan (80°+55° \))=

e. \((Tan100°+Tan(80°))/(1-Tan100°Tan(80°))←Tan (100°+80° \))←=

f. \((Tan 5π/12+Tan π/4)/(1-Tan 5π/12 Tan π/4)←Tan( 5π/12+π/4)←Tan (75°+45° \))=

g. \(Sin π/5 Cos 3π/10 cos π/4+Cos π/5 sin 3π/10 ←Sin (a+b)=Sin (π/5+3π/10)=Sin (36+54 \))=

Solution

a. /(Tan (√3+1)/(1-√3)=-(2-√3)./)

b./( Sin (40°+50°)=Sin90°=1 /)

c. /(Tan (80°+55°)=Tan135°=-1 /)

d. /( Tan (80°+55°)=Tan135°=-1. /)

e./( Tan (100°+80°)←=Tan180° /)

f. /(Tan120°=-√3. /)

g. /( Sin (36+54)=Sin90°=1. /)