Ch-8 Trigonometry | Extra Questions | Class 10th | By Balkishan Sir | - GMS - Learning Simply
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Ch-8 Trigonometry | Extra Questions | Class 10th | By Balkishan Sir |

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 Ch-8 Trigonometry 

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          Chapter-8 [CLASS - 10TH     ]ntroduction to Trigonometry

 Sin(90-𝛉) =Cos𝛉                                     Cos(90-𝛉) = Sin𝛉

Tan(90-𝛉) =Cot𝛉                                     Cot(90-𝛉) = Tan𝛉

Sec(90-𝛉) =Cosec𝛉                                 Cosec(90-𝛉) = Sec𝛉


1) Sin2𝛉 +Cos2𝛉 =1         Tan𝛉 = 𝐒𝐢𝐧𝛉/𝐂𝐨𝐬𝛉           Cot𝛉 = 𝐂𝐨𝐬𝛉𝐒𝐢𝐧𝛉

2) Sec2𝛉 - Tan2𝛉 =1 ,                               3) Cosec2𝛉-Cot2𝛉 = 1


(a+b)(a-b) = a2 - b2

a3 + b3 = (a+b)(a2+b2 -ab)

a3 - b3 = (a-b)(a2+b2 +ab)


Solve the following problems:-

1. In each case of the following find the other trigonometric ratios:

    a) SinA = √𝟑/𝟐                         c) CotA = 𝟓/𝟏𝟐

    b) SecB = 𝟓/𝟑                           d) Cosec A = 𝟏𝟕/𝟖

2. If CosecA = √𝟏𝟎 Then find SecA + TanA. Ans.√𝟏𝟎+𝟏𝟑

3. If Cot𝛉=𝟓𝟏𝟐 show that √𝐬𝐞𝐜𝛉−𝐜𝐨𝐬𝐞𝐜𝛉/√𝐬𝐞𝐜𝛉+𝐜𝐨𝐬𝐞𝐜𝛉 = √𝟕/√𝟏𝟕.

4. If tan𝛂=𝟒𝟑 show that √𝟏+𝐜𝐨𝐬𝛂/√𝟏−𝐜𝐨𝐬𝛂=𝟐.

5. If 𝟒𝐂𝐨𝐬𝛉−𝟏𝟏 𝐒𝐢𝐧𝛉=𝟎 then find 𝟏𝟏𝐂𝐨𝐬𝛉−𝟕 𝐒𝐢𝐧𝛉 / 𝟏𝟏𝐂𝐨𝐬𝛉+𝟕 𝐒𝐢𝐧𝛉.

6. Triangle ABC right angled at C, if tan A=𝟏√𝟑 and tan B=√𝟑 show that
     sinAcosB + cosAsinB=1.

7. Evaluate:- 3sin330°+2cot230°-5cos245°-cot45°.

8. Evaluate:-𝟏/𝐜𝐨𝐬𝟑𝟔𝟎°+𝟏/𝐬𝐢𝐧𝟐𝟔𝟎°−𝟏/𝟐(𝐜𝐨𝐭𝟐𝟒𝟓°)−𝐬𝐢𝐧𝟑𝟗𝟎°.

9. Evaluate:- 𝟑𝐭𝐚𝐧𝟑𝟎−𝐭𝐚𝐧𝟑𝟑𝟎° / 𝟏+𝟑𝐭𝐚𝐧𝟐𝟑𝟎° .

10. Show that 4(sin430°+cos460°)-3(sin245°-cos20°).

11. If cos(2A-B) = sin(A+2B)=√𝟑/𝟐, Find A&B.

12. If 𝛉 is an acute angle and 2sin𝛉-1= 0 then find 3tan2𝛉+8cos2𝛉-5. [0]

13.If sin(2A+45°) = cos(30°-A) then find A.

14. 𝐬𝐢𝐧𝟓𝟎°/𝐜𝐨𝐬𝟒𝟎°+𝐜𝐨𝐬𝐞𝐜𝟒𝟎°/𝐬𝐞𝐜𝟓𝟎°−𝟒𝐜𝐨𝐬𝟓𝟎°/𝐜𝐨𝐬𝐞𝐜𝟒𝟎°.

15. 𝟐𝐬𝐢𝐧𝟒𝟑/°𝐜𝐨𝐬𝟒𝟕°−𝐜𝐨𝐭𝟑𝟎°/𝐭𝐚𝐧𝟔𝟎°−√𝟐𝐬𝐢𝐧𝟒𝟓°.

16. Prove that 𝐭𝐚𝐧𝛉/𝟏−𝐜𝐨𝐭𝛉 + 𝐜𝐨𝐭𝛉/𝟏−𝐭𝐚𝐧𝛉 = 𝟏+𝐬𝐞𝐜𝛉𝐜𝐨𝐬𝐞𝐜𝛉 .

17. Prove that 𝐜𝐨𝐬𝐀−𝐬𝐢𝐧𝐀+𝟏 / 𝐜𝐨𝐬𝐀+𝐬𝐢𝐧𝐀−𝟏=𝐜𝐨𝐬𝐞𝐜𝐀+𝐜𝐨𝐭𝐀.

18. Prove that (1+cotA-cosecA) (1+tanA+secA)=2.

19. If 𝒙/𝒂𝐜𝐨𝐬𝐀+𝒚/𝒃𝐬𝐢𝐧𝐀=𝟏 𝐚𝐧𝐝 𝒙/𝒂𝐬𝐢𝐧𝐀−𝒚/𝒃𝐜𝐨𝐬𝐀=𝟏 𝐭𝐡𝐞𝐧 𝐩𝐫𝐨𝐯𝐞         

       𝒙𝟐/𝒂𝟐+𝒚𝟐/𝒃𝟐 = 2.

20. If sin 𝛉 +sin2 𝛉 =1 then prove that cos2 𝛉 +cos4 𝛉 =1.


About the Author

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s visio…

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