ASSIGNMENT TRIGNOMETRY (CLASS XI)
1. Evaluate : sin2
?
4
+ sin2
3?
5?
+ sin2
4
3?
4
+ sin2
7?
4
3?
2. Prove that : cos x + sin ( 2 + x)- sin ( 2 – x) + cos(? ? ??= 0
3. Find y from the following equation
?
?
?
Cosec ( 2 ? ??+ y cos x cot ( 2 ? ??= sin ( 2 ? ??
???135° ?cos 120°
4. Prove that :
???135° ?cos 120°
= 3 - 2√2
5. If A, B, C are angles of a triangle , prove that
(i)
Sin(A+B) = Sin C
?
(II) cos (
9?
???
2
)= sin
6. Prove that Cos x cos 2 - cos 3x cos 2 = sin4x sin
°
0
°
7. Prove that (i) sin10 sin50 sin70 =
(ii)
1
°
°
°
2
1
(iii) Cos 20° cos 40° ???60° ???80° = 16
?
2
8
3
Sin 20 sin 40 sin60 sin 80 = 16
°
7?
?
?
8. Prove that 4 sin x sin ( 3 – x) sin ( 3 + x) = sin 3x.
9. (cos x + cos y )2 + (sin x + sin y)2 = 4 cos 2 (
sin 5??2 sin 8??sin 11?
???8?
10. Prove that sin 8??2???11??sin 14? = sin 11?
11. If
sin?????
sin?????
1
12. If tanx =
(i)
2
=
???
???
then show that
, find the values of
tan2x
????
????
?
(ii) sin 2x
???
2
)
?
?
(iii) cos 2x
sin 2?
1????2?
(ii) 1?cos 2? = tan2x
13. Prove that (i) 1?cos 2? = tanx
14. Prove that :
(i)
???2?
1????2?
1????2?
= tan x
2?
(ii) 1?cos 2? = tan2 x
15. Show that sin2A + sin2(A + 3 ) + sin2(A ?
?
2?
3
3
) = 2.
3
16. Show that cos2x + cos2(x + 3 ) + cos2(x - 3 ) = 2.
17. Solve the following equations:
(i)
Sin2?+ sin4? +sin6? = 0
(ii)
(iii)
(iv)
(v)
1
Cos ?x cos2? x cos3? =4
√3sin x – cos x = √2
7cos2? + 3sin2? = 4
Tan?+ tan2?+ √3tan?tan2?? =√3
1
1
18. If tanA- tan B = x and cotB – cot A = y prove that cot (A –B) = ? + ?
4 tan ? ?1????2 ??
19. Prove that tan4x = 1?6???2 ?? ???4 ? .
20. Find the value of sin 675◦
21. The minute hand of a clock is 1.5 m long. How far does its tip move in 20 minutes?
22. Convert -
24
5
? radian to degree.
23. Find the value of tan
24. Prove that tan 71◦ =
?
8
cos 26° ?sin 26°
cos 26° ?sin 26°
?
25. If sinxsecx = -√3 and x lie in II quadrant find sin 2 .
26. Without using tables, find the value of 8 cos 320° - 6 cos20°
12
3
27. given that tan x = 5 , cos y = - 5and x, y are in the same quadrant. Calculate
?
(i) Sin(x +y)
(ii) cos 2
?2 ??2
28. α and β are solutions of a cosθ + b sinθ = c then show that cos (α + β) = ?2 ? ?2
29. Sin? + sin ? =a and cos? + cos ? = b, show that
Cos (? ? ? ) =
30. In any
???
?
=
?2 ??2
?2 ??2
ABC prove that
???? ?
?
?
???
?
???
31. Prove that
??????????????
??????????????
=
?? ? ??
??? ??
32. In
ABC prove that: a( b cos C- c cos B)= b2 – c2
33. In
ABC prove that (a-b)2 cos2
?
?
?
+ (a+b)2 sin2 ? = c2