Ashwani Goyal’s Tutorial
SELF ASSESSMENT TEST -4
Class 10+1
TRIGONOMETRY
1. Prove that
cos 9 x  cos 5 x  sin 2 x

sin 17 x  sin 3x cos 10 x
2. Prove that ( sin3A + sinA ) sinA + (cos3A – cosA ) cosA=0
3. Prove that cot4x ( sin5x +sin3x) = cotx ( sin5x – sin3x)
4. Prove that sinx + sin ( x +
2
3
) + sin (x +
5. Prove that cos (  +x ) + cos (  - x ) =
4
4
3
)=0
2 cosx
4
6. Prove that sin 47 + cos 77 = cos 17
A
2
7. Prove that sinA + sin2A + sin4A + sin5A = 4 cos
8. Prove that sin3A + sin2A – sinA = 4 sinA cos
9. Prove that
A
2
2
cos 3A
2
cos 4 A  cos 3 A  cos 2 A
 cot 3 A
sin 4 A  sin 3 A  sin 2 A
10.If sinA = n sin ( A + 2B ) , prove that tan ( A+B) =
1 n
1 n
tanB.
 A B  1
tan
 .
 2  2
11 .If cosA + cosB = ½ and sinA + sinB = ¼ , prove
12.Prove
cos 3A sin3A
      
sin   sin   sin   sin        4 sin
 sin
 2   2
    
 sin
.
  2 
13. Prove that cosA + cos ( A + 2 ) + cos ( A + 4 ) =0
3
3
14. prove cos  cos    sin  sin    4 sin 2      .
2
2
2

15. If sinA + sinB =
3

( cosA – cosB ) prove sin3A + sin3B =0.
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Ashwani Goyal’s Tutorial
16.If cos( A+ B ) sin ( C –D) = cos (A-B) sin (C+D), prove that
tanA tanB tanC + tanD = 0
17. cosec A + secA = cosecB + sec B, prove tanA tanB = cot A  B .
2
18.Prove that
cos 6 A  6 cos 4 A  15 cos 2 A  10
 2 cos A
cos 5 A  5 cos 3 A  10 cos A
19.Prove 2 cos  cos 9 + cos 3 + cos
13
13
13
5
13
20.Prove cos 20 cos 40 cos 60 cos 80 =
=0
1
16
21.Prove that sinA sin ( 60 -A ) sin ( 60 + A ) =
1
4
sin 3A
22.Prove 4 cos 12 cos 48 cos 72 = cos 36 .
23. Prove tan ( 60 + A) tan ( 60 - A ) =
2 cos 2 A  1
2 cos 2 A  1
24.prove sinA sin (B-C ) + sinB sin (C-A) + sinC sin (A-B) =0
25. If A+B = 90 , find the maximum and minimum values of
SinA sinB
Copyright © 2013 GoyalsMath.com .All rights reserved.
Ashwani Goyal’s Tutorial
Copyright © 2013 GoyalsMath.com .All rights reserved.