Trigonometrical Ratios of Some Standard Angles: Simple Problems Set

🔹 01. If θ = 30°, show that cos 2θ = cos²θ − sin²θ.

🔹 02. If , find the value of x.

🔹 03. If α = 60° and β = 30°, show that sin (α + β) = sin α cos β + cos α sin β.

🔹 04. If 4θ = π − 2θ, show that .

🔹 05. If , find the value of sin (θ − 15°), where 0° < θ < 90°.

🔹 06. If θ is a positive acute angle and sin (θ + 18°) = 1/2, find the value of θ, where 0° < θ < 90°.

🔹 07. If tan (θ − 15°) = 1, find the value of cos θ.

🔹 08. If sin (3θ − α) = 1 and cos (2θ + α) = 1/2, find the value of tan θ.

🔹 09. If sin θ + cosec θ = 2, find the value of cos (θ − 60°).

🔹 10. Find the value of .

🔹 11. Prove that .

🔹 12. Prove that .

🔹 13. Find the value of .

🔹 14. If , find the value of x.

🔹 15. Find the value of .

🔹 16. Find the simplest value of .

🔹 17. Solve .

🔹 18. If , find the value of x.

🔹 19. Prove that .

🔹 20. If , find the value of x.

🔹 21. Find the value of x when .

🔹 22. Find the value of .

🔹 23. If α and β are positive acute angles, find the values of α and β in degrees when sin (2α − β) = 1 and cos (α + β) = 1/2.