Math test

1.In a △ ABC, right-angled at B, AB = 24 cm , BC = 7 cm. Determine

(i) sin A , cos A (ii) sin C, cos C. Ans : 7/25&24/25. Ans : 24/25&7/25

2.If tanθ=a/b,find the value of (cos θ + sin θ)/ (cos θ – sin θ). Ans : (a+b)/(a-b)

3. In △PQR, right-angled at Q, PQ = 4cm and RQ = 3 cm. Find the value of
sinP, sin R, sec P and sec R. Ans: 3/5 , 4/5, 5/4&5/3

4. sin2 30∘ + sin2 45∘ + sin2 60∘ + sin2 90°. Ans:5/2

5. 4(sin4 60∘ + cos4 30∘) − 3(tan2 60∘ − tan2 45∘) + 5cos2 45°. Ans :1

6. 4(sin4 30∘ + cos2 60∘) − 3(cos2 45∘ − sin2 90∘) − sin2 60° Ans : 2

7. cos θ/ (1 – sin θ) = (1 + sin θ)/ cos θ

8. cos θ/ (1 + sin θ) = (1 – sin θ)/ cos θ

9. (1 – sin θ) / (1 + sin θ) = (sec θ – tan θ)^2

10.



11. 1 – cos θ/ sin θ = sin θ/ 1 + cos θ

12.




13. tan2 θ − sin2 θ = tan2 θ sin2 θ

14. (cosec θ + sin θ)(cosec θ – sin θ) = cot2θ + cos2θ

15. cosec (A – sin A)(sec A – cos A)(tan A + cot A) = 1

16. sec A(1- sin A) (sec A + tan A) = 1

17. (sec θ + cos θ) (sec θ – cos θ) = tan2 θ + sin2 θ

18. (1 + tan2 θ)(1 – sin θ)(1 + sin θ) = 1