If sinθ and cosθ are the roots of the equation ax2 - bx + c = 0, then a, b and c satisfy the relation
a2 + b2 + 2ac = 0
a2 - b2 + 2ac = 0
a2 + c2 + 2ab = 0
a2 - b2 - 2ac = 0
If sinθ + cosθ = 0 and 0 < θ < π, then θ
0
π4
π2
3π4
The value of cos15° - sin15° is
12
- 12
122
The period of the function f(x) = cos4x + tan3x is
π
π3
If x + 1x = 2cosθ, then for any integer n, xn + 1xn is equal to
2cosnθ
2sinnθ
2icosnθ
2isinnθ
Prove that the equation cos(2x) + asin(x) = 2a - 7 possesses a solution if 2 ≤ a ≤ 6.
Find the values of x. - π < x < π, x ≠ 0 satisfying the equation,
g1 + cosx + cos2x + ... ∞ = 43
The value of cotx - tanxcot2x is
1
2
- 1
4
B.
Given, cotx - tanxcot2x = cosxsinx - sinxcosxcos2xsin2x = cos2x - sin2xsin2x2sinxcosx . cos2x = 2cos2xsin2x2sinxcosx . cos2x = 2 ∵ cos2x - sin2x = cos2xand 2sinxcosx = sin2x
The number of points of intersection of 2y = 1 and y = sin(x), in - 2π ≤ x ≤ 2π is
3
If cosA3 = cosB4 = 15, - π2 < A < 0, - π2 < B < 0 then value of 2sinA + 4sinB is
- 2
- 4