alok vidyashram summer vacation holiday homework 2012

ALOK VIDYASHRAM
SUMMER VACATION HOLIDAY HOMEWORK 2012
CLASS: X SLC
SUBJECTS
ENGLISH
MATHEMATICS
OPT. MATHS
HOMEWORK
Make a brochure of any interesting place near your locality.
Do the exercises of unit 1 & 2
Sets: H.C. F and LCM Simplification, compound Interest , SEDIPS,
NPABSON, SOS, JST, PABSON, 2068 (CENTRAL, Eastern) from 10
sets.
Prove that:
1. Cos (π/4+A)= 1/r 2 (cos-sinA)
2. Sin /45A) +cos (45+)= r 2 cosA
3. Cos((π/4)-sin ((π/4-A)=o
4. Sin 2 (45+A)+sin 2 (45-A)=01
tan A + tan B sin( A + B)
5.
=
tan A _ tan B cos( A + B)
6.Cos(A+B)cos(A+B)=cos 2 A-sin 2 B=cos 2 B-sin 2 A
2
2
tan A − tan B sin A − sin B
7.tan(A+B) tan(A-B)=
=
2 2
2
2
1−
tan A.tan
B cos B − sin B
8. tan 2 A – tan 2 sin( A + B).sin(sin−
B)
B=
2
cos A.cos
B
1 1
2
9. − = cosec
A
2
tan A tan A
cos λ sin λ
10. = = cos3λ
sec λ cosecλ
11. if tan λ =5/6 and tanβ=1/11 show that λ +β= π/4
12. if, A+B=π/4, prove that:
i)cotA.cot +B-cotA-cotB=1
ii) (cotA-1) (cotB-1)=2
13.i) if sin (θ+φ=2sin(θ-φ), prove that:
tanθ=3tanφ
ii) If tan λ =k tanβ, prove that:
(k+1)sin ( λ -β)= (k-1) sin( λ +β)
12. Prove thatL cos 2 (π/4- λ /4)-sin4π/4- λ /4)=sin λ /2
13. (cosA-cosβ) 2 +(sinA-sinβ) 2 =4sinβ) 2 =4sin 2 A − B
2
14.if cos cos λ /3=1/2(a+1/a) show that cos λ =1/2 (a 3 +1/a 3 )
15. 1-2sin 2 (π/4-A/2)= sinA
16. if sin ( λ +β)= k sin( λ -β), Prove that
17. if cos+cosy=1/3 and sinx+siny=1/4 prove that.
x + y
Tan = 3/ 4
2
18.(cosβ-cos λ ) 2 +(sin λ -sinβ) 2 λ − β
=4sin2 ( )
2
19. Sin 2 A+sin 2 B+2sinA.sinB cos(A+B)=sin 2 A(A+B)
20. sinx 2 +sin 2 ( λ +120)+sin 2 ( λ -120)=3/2
21.cos20.cos40.cos80=1/8
22. sin10.cos20.sin30.cos40-1/16