DCM
PRESIDENCY SCHOOL, LUDHIANA
MATHS – ASSIGNMENT, CLASS-
11TH TOPIC - TRIGONOMETRY
1.
Find the value of
(a) sin 315 (b)
cos 210 (c) sin (-1125)
2.
If 2tanβ + cot β = tan α , prove that cot β = 2 tan(α
- β).
3.
If A + B = π/4 , Prove that ;
(i) (1 + tanA) (1 – tan B) = 2 (ii) (cotA - 1)(cot B - 1) =2
4.
If tan ( α +β) = n tan(α - β) , show that (n + 1)sin
2β = (n -1) sin 2α
5.
If tan A – tan B = x and cot B – cot A = y , prove
that cot(A - B) = 1/X + 1/y
6.
Prove that cos 20 cos 40 cos 60 cos 80 = 1/16
7.
Prove that sin 10 sin 30 sin50 sin70 = 1/16
8.
Prove that sin 20 sin 40 sin 60 sin80 = 3/16
9.
Prove that sin A sin ( 60 -A) sin (60 + A) = ¼ sin 3A
10. Prove that 1
+ cos 2x + cos 4x + cos 6x = 4 cos x cos2x cos 3x
11. Prove that
tan α + 2tan 2α + 4 tan 4α + 8cot 8α = cotα.
12. Prove that
cos2A + cos2(A + 2π/3) + cos2 (A - 2π/3) = 3/2
13. Prove that
cos α + cosβ + cos γ + cos (α +β +γ) = 4 cos α +β /2 cos β +γ/2 cos γ +α/2
14. Prove that
sinx /sin 3x + sin 3x /cos 9x + sin 9x /cos27x = ½ (tan 27x - tanx)
15. If cos α
+cos β + cosγ = 0 then prove that ,
cos3α + cos 3β + cos 3γ = 12 cosα cosβ cosγ
16. Solve the following
equations
(i)
4 cos A - 3 sec
A = tan A (ii) tan θ
+ tan 2θ + tanθ tan2θ = 1
(iii) tan θ + tan 2θ + tan 3θ = tanθ tan2θ tan
3θ
17 Prove
that tan 70 = tan 20 + 2 tan 50
18 Prove that sinα + sin (α + 2π/ 3 ) + sin ( α
+ 4π/ 3) = 0
19. If sin α
+ sinβ = a and cosα + cosβ = b prove
that cos (α -β) = a2 + b2
– 2 /2
20 If 3 tan A tan B = 1 ,
prove that 2 cos ( A + B) = cos ( A - B
)
21. 4 Sin α
Sin ( α + π/3) Sin (α + 2π/3 ) = Sin 3α.
22. If A+ B+
C = 180 Prove that Sin 2A + Sin 2B – Sin 2C = 4 Cos A Cos B Sin C
23.Prove
that Sin 51 + Cos 81 = Cos 21
24. Prove
that tan A + tan( 60 + A) + tan(120 + A) = 3 tan 3A
25. Solve
the equation Cos 3x + 8 Cos3x
= 0
