Questions For Practise For Optional Maths

# Short-Answer Questions:

Find the values of 

Sin15o
Tan750
Sin750
Cos75o
Tan105o
Cos150+Cos75


Show that:

Cos400- Sin400 = Sin50
 Cos15o-Sin15o = 
Sin105o+Cos105o = 
Cos500 + Cos700 = Cos100
Tan15o + Cot15o = 4
Sin105o + Cos75o = 
Tan75o +Cot75o = 4
Cos(400+) – Sin(500-) = 0
 = tan100
 = Cot500


Solve the following

If CosA =  and CosB = , find the value of:
Sin (A-B)                   
Cos (A-B)                       
If CosA =  and CosB =  ,find the value of:
Cos (A+B)     
Sin (A-B)

# Long-Answer Questions:

Prove the following identities:






Prove that:

Sin (45o+ ) +Cos (45o+ ) =  Cos
Cot (45o+ ) = 
Sin (A-45o) = 
Tan (45o+A) tan (45o-A) = 1
Sin2 (45o+A) +Sin2 (45o-A) = 1

Solve the following problems.   
If tan A =  and tanB = , show that A+B = 
If tanA =  and tanB = , show that A+B = 
If tanA = , show that A+B = 
If tanA =   show that A+B = 
Prove the following: 

Cos18o-Sin18o =  Sin27o
Cos55o + Cos35o = Cos10o


Prove the following:






Show that:
Tan20o+tan25o+tan20otan25o=1
Tan20o+tan72o+tan88o = tan20o.tan72otan88o
Tan3A-tan2A-tanA = tan3A.tan2A.tanA
If (A+B) = 45o, show that :
(1+tanA) (1+tanB) = 2
(CotA-1) (CotB-1) = 2