MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C8B12A.670283E0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C8B12A.670283E0 Content-Location: file:///C:/117AEA50/trigonometry10.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" MATHEMATICS CLASS X

               &= nbsp;           &nbs= p;       

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;

TRIGONOMETRY

 

Trigonometry Ratios

&nbs= p;

Prove tha= t

&nbs= p;

1.         = (Sec2q-1) (1-Cosec2= q)=3D-1

&nbs= p;

2.         = (1+Cot = q-Cosecq) (1+Tan= q+secq)=3D2

&nbs= p;

3.         = (Cosecq-Sinq) (sec= q-Cosq) (Tan= q+Cotq)=3D1

&nbs= p;

4.         =

&nbs= p;

5.         =

&nbs= p;

6.         = =3DTanq

&nbs= p;

7.         = (Tanq-Cotq)=3D

&nbs= p;

8.         = (-tanq+Cotq) =3D

&nbs= p;

9.         = 7+Tan2A +Cot2 A=3D (SinA +CosecA)2 +(CosA +SecA)2   

&nbs= p;

10.       (Cose= cq–Cotq)

&nbs= p;

11.       =

&nbs= p;

12.       =

&nbs= p;

13.       =

&nbs= p;

14.       = =3D 2 Secq

&nbs= p;

&nbs= p;

 

15.       (1+Cos A) (1-Cos A) (1+Cot2A)=3D1

&nbs= p;

16.       = =3D

17.       (Cose= cq–Sinq) (Sec= q-Cosq)=3D

&nbs= p;

18.       =

&nbs= p;

19       

&nbs= p;

&nbs= p;

20        (1-Sinq+Cosq)2=3D2(1+Cosq) (1-Sinq)

&nbs= p;

21.       =

&nbs= p;

22.       =

&nbs= p;

23.       If x = =3D a Sin= q + b Cos= q and y =3D a Cos q – b Sin q. Prove that x2+y2 =3D a2+b2

&nbs= p;

24.       If Si= nq + Cosq =3D p and Secq + Cosecq =3D q, show that q(p2-1)=3D2p

&nbs= p;

25.       If Ta= n + Sin =3Dm and Tan-Sin=3D n show that m2-n2=3D4

&nbs= p;

26.       If x= =3Dr SinaCosb, y=3D r Sin= aSinb and z=3D rcos= a, prove that r2 =3D x2+y2+z2

&nbs= p;

27.       If Si= nq+Sin2q =3D1, prove that Cos2q + Cos4q =3D1

&nbs= p;

28.       If (S= ecq+Tanq)=3Dm and (Sec= q–Tanq)=3Dn, show that mn=3D1

&nbs= p;

2= 9.      =         If Sinq+Cosq=3DSin(90-q) show that Cotq=3D

        &= nbsp;           &nbs= p;            &= nbsp; 

30        tanA  -   tanB =3D         =

 

= 31.      =         Prove that

          &= nbsp;  (CBSE 2006)

 

 

 

 

&nbs= p;

        &= nbsp;   Trigonometric ratios of complementary angles

&nbs= p;

Without u= sing trigonometric tables prove that

&nbs= p;

32.       Sec70= o Sin 20o+Cos 20o Co= sec70o=3D2

&nbs= p;

33.       Sin(5= 0o+q)–Cos(40o–q)=3D0 

&nbs= p;

34.       Tan7<= sup>o Tan23o Tan60o Tan67o Tan83o=3D<= sub>

&nbs= p;

35.       Cot12= o Cot 38o Cot 52o Cot 60o Cot 78o= =3D

36.       =

&nbs= p;

37..      Sec2 10–Cot2 80 +

&nbs= p;

38.      

&nbs= p;

39.       

&nbs= p;

40.     2Sin 45=3D0

&nbs= p;

41      Tan(55o-q)-Cot (35o+= q) =3D0

&nbs= p;

42.   

&nbs= p;

43.       =

&nbs= p;

Evaluate<= /p>

44. =

&nbs= p;

45     &= nbsp;  (CBSE 2006)

46. Without using trigonometrical tables, evaluate the following:

-  ( CBSE 2008)

4= 7.      =         Prove that         =            ( CBSE 2008)

= 48.  Prove that  ( 1+cot A – cosec = A)(1+ tanA + secA)=3D2     <= /span>( CBSE 2008)

 

&nb= sp;

 

        &= nbsp;  

&nbs= p;

&nbs= p;

( 1 mark questions)

= 1.     Given that tan =3D , what is the value of&= nbsp;  ?=

= 2.     What is the maximum value of  ?=

= 3.     In a triangle ABC, right angled at C, if tanA =3D  what is the value of cotB?=

= 4.     If 5tanα= ; =3D 4, find the value of   =

= 5.     Evaluate  .=

= 6.     If tanq +  =3D 2, fin= d the value of tan2= q +  .=

= 7.     In a triangle ABC,= right angled at B, if sinA =3D  , find all= the trigonometric ratios of C.

= 8.     If secA + tanA =3D p, express secA, tanA and sinA in terms if p.=

= 9.     If sin(A + B= ) =3D sinAcosB + sinBcosA, find the value of= sin75.

= 10.  If= cos(A - B) =3D cosAcosB + sinAsinB, find the value of= cos15.

= 11. An equilateral triangle is inscribed in a circle of 6cm. Find its side.

= 12. Prove:

i)&n= bsp;       (sin= q + sec<= /i>= q)2 + (cos= q + cosec= q)2 =3D (1 + sec= qcosec= q)2

ii)&= nbsp;      =3D tanq + cot= q=

iii)=     secA + tanA =3D

iv)&= nbsp;    =3D tanq

v)&n= bsp;      =3D cosecq + cot= q=


&nbs= p;

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