The document Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev is a part of the Class 10 Course Class 10 Mathematics by VP Classes.

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**VERY SHORT ANSWER TYPE QUESTIONS**

**Q1. If cotÎ¸ = 7/8 then what is the value of **

**Q2. If tan A then find sin A.**

**Sol.** In a right Î” ABC (âˆ B = 90Â°), Hypotenuse = AC, Base = AB and Perpendicular = BC.

Since,

Using Pythagoras theorem, we have:

**Q3. Evaluate cos 60Â°Â· sin 30Â° + sin 60Â°Â· cos 30Â°.**

**Sol. **We have:

cos 60Â°Â· sin 30Â° + sin 60Â°Â· cos 30Â°

**Q4. If tan A = cot B, prove that A + B = 90Â°.**

**Sol.** âˆµ tan A = cot B

âˆ´ tan A = tan (90Â° âˆ’ B)

â‡’ A = 90Â° âˆ’ B

â‡’ A + B = 90Â°.

**Q5. Express sin 67Â° + cos 75Â° in terms of ratios of angles between 0Â° and 45Â°. Sol. **âˆµ 67Â° = 90Â° âˆ’ 23Â° and 75Â° = 90Â° âˆ’ 15Â°

âˆ´ sin 67Â° + cos 75Â° = sin (90Â° âˆ’ 23Â°) + cos (90Â° âˆ’ 15Â°) = cos 23Â° + sin 15Â°.

**Q6. In the given figure, AC is the length of a ladder. Find it.**

**Sol.** Let AC =x = [Length of ladder]

âˆ´ In right Î” ABC,

Thus, the length of the ladder is 2âˆš3 m

**Q7. If sin Î¸ = 12/13 , find the value of: **

**Q8. In the given figure, find BC.**

**Sol.** In Î” ABC,

**Q9. In Î” ABC, if AD âŠ¥ BC and BD = 10 cm; âˆ B = 60Â° and âˆ C = 30Â°, then find CD.**

**Sol. **In right Î” ABD, we have

**Q10. In the given figure, ind AC, if AB = 12 cm.**

**Q11. In the given figure, Î” ABC is a right triangle. Find the value of 2 sinÎ¸ âˆ’ cosÎ¸. Sol.** We have right Î” ABC,

**Q12. In the figure, find sinA.**

**Sol. **In right Î” ABC,

**Q13. What is the value of sinÎ¸. cos(90Â° âˆ’ Î¸) + cosÎ¸ . sin(90Â° âˆ’ Î¸)?**

**Sol. **sinÎ¸ Â· cos(90Â° âˆ’ Î¸) + cosÎ¸ Â· sin(90Â° âˆ’ Î¸) = sinÎ¸ Â· sinÎ¸ + cosÎ¸ Â· cosÎ¸

[âˆµ cos(90Â° âˆ’ Î¸) = sinÎ¸ , sin(90Â° âˆ’ Î¸) = cos Î¸]

= sin^{2} Î¸ + cos^{2} Î¸

= 1

**Q14. Show that: tan 10Â° tan 15Â° tan 75Â° tan 80Â° = 1**

**Sol.** We have:

L.H.S. = tan 10Â° tan 15Â° tan 75Â° tan 80Â° =

tan (90Â° âˆ’ 80Â°) tan 15Â° tan (90Â° âˆ’ 15Â°) tan 80Â°

= cot 80Â° tan 15 cot 15Â° tan 80Â° = (cot 80Â° Ã— tan 80Â°) Ã— (tan 15Â° Ã— cot 15Â°)

= 1Ã— 1

= 1 = R.H.S.

**Q15. Find the value of:**

**Sol.** We have:

**Q16. Write the value of: **

**Q17. Write the value of: **

**Q18. If sec ^{2} Î¸ (1 + sin Î¸) (1 âˆ’ sinÎ¸) = k, find the value of k.**

**Q19. If sin then find the value of (2 cot ^{2} Î¸ + 2).**

**Sol. **2 cot^{2} Î¸ + 2 = 2 (cot^{2} Î¸ + 1) = 2 (cosec^{2} Î¸)

**Q20. If cos A = 3/5, find 9 cot ^{2} A âˆ’ 1.**

**Q21. If sin 3Î¸ = cos (Î¸ âˆ’ 6)Â° and 3Î¸ and (Î¸ âˆ’ 6)Â° are acute angles, find the value of Î¸.**

**Sol. **We have:

sin3Î¸ = cos(Î¸ âˆ’ 6)Â° = sin[90Â°âˆ’(Î¸ âˆ’ 6)Â°]

âˆµ [sin (90Â° âˆ’ Î¸) = cos Î¸]

â‡’ 3Î¸ = 90Â° âˆ’ (Î¸ âˆ’ 6)Â°

â‡’ 3Î¸ = 90 âˆ’ Î¸ + 6

â‡’ 3Î¸ + Î¸ = 96

**Q22. If tan Î¸ = cot (30Â° + Î¸ ), find the value of Î¸ .**

**Sol. **We have:

tan Î¸ = cot (30Â° + Î¸)

= tan [90Â° âˆ’ (30Â° + Î¸)]

= tan [90Â° âˆ’ 30Â° âˆ’ Î¸]

= tan (60Â° âˆ’ Î¸)

â‡’ Î¸ = 60Â° âˆ’ Î¸

â‡’ Î¸ + Î¸ = 60Â°

**Q23. If sinÎ¸ = cosÎ¸ , find the value of Î¸ .**

**Sol. **We have:

sinÎ¸ = cosÎ¸

Dividing both sides by cosÎ¸, we get

â‡’ tan Î¸ = 1 ...(1)

From , the table, we have:

tan 45Â° = 1 ...(2)

From (1) and (2), we have:

Î¸ = 45Â°.

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