Self Assessment Test-2

Ashwani Goyal’s Tutorial
SELF ASSESSMENT TEST -2
Class 10+1
TRIGONOMETRIC FUNCTIONS
1.Evalute; (a) cos 75 (b) sin 15
2. Prove that tan 15 + cot 15 =4.
3. Prove that cot2A + tanA = cosec2A.
4. Prove that tan 75 - tan 30 - tan 75 .tan 30 = 1
5. Prove that tan3A – tan2A – tanA = tanA tan2A tan3A.
6. Prove that tan 65 = tan 25 + 2 tan 40
7. Prove that




cos 29  sin 29
cos 29  sin 29

 tan 74
8. If A – B = 45 , show that (1 + tanA) (1 + tanB ) = 2 tanA
9. If tanA = k tanB , then prove that sin(A-B) =
10. Prove that tan


  
4

k 1
sin  A  B 
k 1
tan  3    = -1
 4

11. Find the value of sin(A+B), cos(A-B), tan(A-B) given that tanA = 2 ,
cosB =

3
5
where 180  A270 and 90  A180 .
12.Prove that sin 2    A   sin 2    A  
8 2
8 2
1
sin A
2
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13.Evaluate cos2    A   sin 2    A 
4

4

 13 


 12 
14. Prove that tan
15. If cos A =
1
7
=2-
and cos B =
3.
13
14
( A, B being positive acute ) , prove that
A – B = 60
16. If tanA =
a
a 1
and tanB =
1
,
2a  1
prove A + B = 45
17.If tanA + tanB =a and cotA + cotB =b then prove that
Cot (A+B) =
1 1
  .
a b
18. Prove that cosA – sinA =


2 cos A  
4

19.If tan(A+B) = p and tan (A- B) =q then prove tan2A =
20.If cotA cotB =2 , show
21.If
sin  A  B  a  b

sin  A  B  a  b
pq
1  pq
cos A  B  1

cos A  B  3
, then show that
tan A a

tan B b
22.Prove that : cos2A cos2B + sin 2  A  B  sin 2  A  B = cos2(A +B)
23.If 2 tanB + cotB = tanA , prove that cotB = 2 tan (A-B)
24. If cos (A +B) sin (C + D ) = cos (A – B ) sin( C- D ) , prove that
CotA cotB cot C = cot D
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Ashwani Goyal’s Tutorial



25. Prove that cos 33 cos 57
21 
69
sin
sin
2
2
2
2

2

 2
2
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