Trigonometric ratios Questions

What is (sin 9° – cos 9°) equal to?

Consider the following numbers:

(I) tan22.5°

 (II) cot22.5°

 (III) tan22.5° – cot22.5°

 How many of the above are irrational numbers?

Direction for Questions (41-43):

Consider the following for the three (03) items that follow

: Let p = sin 35°, q = sin 25° and r = sin(–95°).

What is (p² + q² + r²) equal to?

For the following two (02) items:

Let p = cosec 20° and q = cosec 70°.

What is equal to?

What is the value of

What is the value of sinq if q is the acute angle between the lines whose equations are px + qy = p + q and p(x - y) + q(x + y) = 2q?

The number of integer values of k, for which the equation 2 sin x = 2k + 1 has a solution, is

If tan x = −3/4 and x is in the second quadrant, then what is the value of sin x cos x ?

What is the value of the following? cosec(7π/6) · sec(5π/3)