Trigonometric ratio se related Questions with solutions

                Trigonometry - 4     

Hello friends ! Maine last post me aapko Basic of trigonometric ratio k baare me full details me bataya tha. Ussi topic ko aage badate huye aaj mai aapko trigonometric ratio se related question with solution bataunga.

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Shirf bataunga hi nhi balki aapko solve karna bhi shikhaunga. Aur Mujhe puri ummid hai ki, agar aapne carefully samjh liya to aap bhi trigonometric ratio se related question ko easily kar paayenge. To  kya aap ready hai ? aayiye shikhate hai -:

Trigonometric ratio se related questions with solution 

Q-1.  ∆ABC me /_B = 90° hai. AC = 10 aur BC = 6 ,  to "sinθ" ki value batayiye.

Figure-1

Solution-:  Figure-1 , me aap dekh sakte hai ki , lamb BC = 6 aur karn AC = 10 . Hum jaante hai ki ,
                 sinθ = lamb/karn
                          = BC/AC
                          = 6/10
                          = 3/5
Isliye , sinθ = 3/5      Answer.

Q-2. ∆ABC me /_B = 90° hai.  AB = 3 aur BC = 7 , to "tanθ" = ??

Figure-2

Solution -: Figure-2 se, lamb BC = 7 aur Aadhar AB = 3 
Formula use karte hai -:
              tanθ = lamb/Aadhar
                        = BC/AB
                        = 7/3
Isliye , tanθ = 7/3      Answer.

Q-3. ∆ABC me /_B = 90° hai. AC = 5 and BC = 3 ho to "cosθ"  ki value batayiye.

Figure-3

Solution-: Figure-3 me "θ" , /_C par hai. Isliye "θ" k front side AB ko lamb kahenge aur side BC aadhar hoga. Ab formula use karte hai -:
                  cosθ = Aadhar/karn
                            = BC/AC
                            = 3/5
Isliye , cosθ = 3/5     Answer.

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Q-4.  Figure-4 ki help se "cosec A" ki value bataye.

Figure-4

Solution-:  Hume cosec A ki value batani hai aur /_A ki front side lamb BC aur Aadhar AB hoga.
Fig. me diya hai -:
Karn AC = 13
Lamb BC = 5
Ab hum jaante hai ki ,
             cosec A = karn/lamb
                            = 13/5
Isliye , cosec A = 13/5     Answer. 

Q-5. Fig.-5 ki help se "sec C" ki value find kariye.

Figure-5

Solution-: /_ C k liye karn AC = 12 aur Aadhar BC = 6 hoga.
Formula -:  
            sec C = Karn/Aadhar
                       = 12/6
                       = 2
Isliye , sec C = 2    Answer.



Q-6. Fig.-6 se "cot C" ka maan gyat kijiye.

Figure-6

Solution -: /_ C k liye Aadhar BC = 6 aur lamb AB = 15 hoga.
Formula -:
              cot C = Aadhar/lamb
                         = 6/15
                         = 2/5
Isliye , cot C = 2/5     Answer.

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Q-7. fig.-7 ki help se "sin A" , "cos C aur "tan A" ki value bataye.

Figure-7

Solution-:   from fig.-7
/_A k liye , lamb BC = 8 aur Aadhar AB = 6 .
Sin A = l/k
           = BC/AC
           = 8/10
           = 4/5
Isliye , sin A = 4/5     Answer.
tan A = l/A
           = BC/AB
           = 8/6
           = 4/3
Isliye , tan A = 4/3       Answer.
/_C k liye, Lamb AB = 6 aur Aadhar BC = 8 .
cos C = A/K
           = BC/AC
           = 8/10
           = 4/5
Isliye , cos C = 4/5     Answer.

Q-8.  fig.-7 se , "sin C × cosec A "  ki value bataye.

Solution-: from fig.-7
/_C k liye , Lamb AB = 6 aur Aadhar BC = 8 .
Sin C = L/K
           = AB/AC
           = 6/10
           = 3/5
cosec A = K/L
               = AC/BC
               = 10/8
               = 5/4
Ab sin C × cosec A = (3/5)×(5/4)
                                   = 3/4
Isliye , sin C × cosec A = 3/4    Ans.

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Q-9. Fig.-7 ki help se 
"tan A + sec C = ??

Solution-:   tan A = L/A
                                = BC/AB
                                = 8/6
                               = 4/3
sec C = K/A
          = AC/BC
          = 10/8
          = 5/4
tan A + sec C = (4/3)+(5/4)
                         = (16+15)/12
                         = 31/12
Isliye ,  tan A + sec C = 31/12    Ans.



Q-10. Fig.-7 ki help se ,
 cos C - cot A = ??

Solution -: from Q-7 ,  cos C = 4/5
cot A = A/L
          = AB/BC
          = 6/8
          = 3/4
Ab  cos C - cot A =  (4/5)-(3/4)
                               = (16-15)/20
                               = 1/20
Isliye, cos C - cot A = 1/20  Ans.

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