Value of Trigonometric Functions at Multiples and Submultiples of an angle – Fill in the Blanks Type Questions (FBQs) Exercise Solutions

1. If {1 – tan² ( π/4 – x )}/{1 + tan² ( π/4 – x )} = sin kx, then k = ………. Watch Solution
2. If cos x cos 2x cos 2² x ……….. cos 2^n–1 x = λ sin 2^n λ/sin x , then λ = ……….. Watch Solution
3. The value of cos 2π/15 cos 4π/15 cos 8π/15 cos 16π/15 is ………… Watch Solution
4. If tan x = (1 – cos y)/sin y , then tan 2x = …………………….. Watch Solution
5. If k = sin π/18 sin 5π/18 sin 7π/18, then the numerical value of k is ………….. Watch Solution
6. In a triangle ABC with ∠C = π/2 the equation whose roots are tan A and tan B is …………. Watch Solution
7. The value of cos² 48° – sin² 12° is ……………………. Watch Solution
8. The least value of 2 sin² θ + 3 cos² θ is ……………………….. Watch Solution
9. If cos⁶ x + sin⁶ x + k sin² 2x = 1, then k = ………………….. Watch Solution
10. The value of (1 + cos π/8)(1 + cos 3π/8)(1 + cos 5π/8)(1 + cos 7π/8) is…………………………. Watch Solution
11. The value of (cot x – tan x)/cot 2x is …………………….. Watch Solution
12. If tan θ = t, then tan 2θ + sec 2θ = ……………………. Watch Solution
13. If tan θ = a/b , then a sin 2θ + b cos 2θ is equal to ………………… Watch Solution
14. If tan x = 1/7 , tan y = 1/3 and cos 2x = sin ky, then k = …………………. Watch Solution
15. The value of cos π/5 cos 2π/5 cos 4π/5 cos 8π/5 is ……………………… Watch Solution
16. The value of sin 3π/10 is ……………………….. Watch Solution
17. The value of cos² 6° – cos² 24° is ………………….. Watch Solution
18. If π/2 less than x less than π, then √(1 – cos 2x)/(1 + cos 2x) = ………………………… . Watch Solution
19. If π/4 less than x less than π/2, then √2 + √2 + 2 cos 4x = ………………………… . Watch Solution
20. The value of 108 sin π/9 – 144 sin 3π/9 is ………………………… . Watch Solution