Today our topic of discussion is Trigonometric Ratio Exercises 9.1.
Trigonometric Ratio Exercises 9.1
Exercise 9.1
- Verify whether each of the following mathematical statements is true or false. Give argument in favour of your answer.
1) The value of tan A is always less than 1.
2) cot A is the multiplication of cot and A
3) For any value of A, sec A = 12/5
4) cos is the smallest form of cotangent
- If sinA = 3/4 find the other trigonometric ratios of the ∠A.
- Given that, 15cot A = 8 find the values of sin A and sec A.
- If ∠C is the right angle of the right-angled ΔABC, AB = 13cm, BC = 12 cm and ∠ABC = θ , find the values of sinθ, cosθ and tanθ.
- ∠B is the right-angle of the right angled tringle ABC. If tan A = √3, verify the truth of √3sin A. cos A = 3/4 .
Prove (6-20):
6.
1) 1/(sec² A) + 1/(cosec²A) = 1
2) 1/(cos² A) – 1/(cot² A) = 1
3) 1/(sin² A) – 1/(tan²A) = 1
7.
1) (sin A)/(cosec(A)) + (cos A)/(sec(A)) = 1
2) (sec(A)/(cos A) – (tan A)/(cot A) = 1
3) 1/(1 + sin²A) + 1/(1 + co * sec² A) = 1
8.
1) (tan A)/(1 – cot A) + (cot A)/(1 – tan A) = secA.cosecA + 1
2) 1/(1 + tan² A) + 1/(1 + cot² A) = 1
9. (cos A)/(1 – tan A) + (sin A)/(1 – cot A) = sin A + cos A
10. tan A * √(1 – sin² A) = sin A
11. (secA + tan A)/(cosecA + cot A) = (cosecA – cot A)/(secA – tan A)
12. (cosecA)/(cosec(A) – 1) + (cosec(A))/(cosec(A) + 1) = 2sec² A
13. 1/(1 + sin A) + 1/(1 – sin A) = 2sec² A
14. 1/(cosec(A) – 1) – 1/(cosec(A) + 1) = 2tan² A
15. (sin A)/(1 – cos A) + (1 – cos A)/(sin A) = 2cosec(A)
16. (tan A)/(sec(A) + 1) – (secA – 1)/(tan A) = 0
17. (tanθ + sec(θ )² = (1 + sin θ )/(1 – sin θ )
18. (cot A + tan B)/(cot B + tan A) = cot A * tan B
19. √((1 – sin A)/(1 + sin A)) = sec(A) – tan A
20. √(secA + 1)/(secA – 1)) = cot A + cosecA
21. If cos A + sin A = √(2) * cos A prove that, cos A – sin A = √2sin A
22. If tan A = 1/(√3)) find the value of (cosec² A – sec² A)/(cosec² A + sec² A)
23. If cosec(A) – cot A = 4/3 what is the value of cosec A + cot A
24. If cot A = b/a find the value of asin A – bcos A asin A+ bcos A
25. If cosec A – cot A = 1/x
1) find the value of cosec A + cot A
2) Show that, sec A = (x²+ 1)/(x² – 1)
3) According to the stimulus prove that, tanA + cot A = secA cosecA
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