Equations Involving sinx + cosx and sinx.cosx
Trending Questions
Q.
If sin x + cos x = t, then sin x cos x is equal to
t2−12
t2+12
√2−t2
√t2−1
Q. The sum of all the values of θ (0≤θ≤2π) which satisfies both the equations rsinθ=3 and r=4(1+sinθ) is
- π6
- 5π6
- π
- π2
Q. Consider the system of equations
xcos3y+3xcosysin2y=14
xsin3y+3xcos2ysiny=13
The number of values of y∈[0, 6π] is
xcos3y+3xcosysin2y=14
xsin3y+3xcos2ysiny=13
The number of values of y∈[0, 6π] is
- 5
- 3
- 4
- 6
Q. The number of integral values of n such that sinx(sinx+cosx)=n has atleast one real solution is
- 4
- 1
- 3
- 2
Q. The equation
2cos2x2sin2x=x2+x−2;0<x≤π2
has
2cos2x2sin2x=x2+x−2;0<x≤π2
has
- No real solution
- One real solution
- more than one solution
- none of these
Q. If x and y satisfy the equation 12sinx+5cosx=2y2−8y+21, then the value of 12cot(xy2) is
Q. Number of common solution(s) of the trigonometric equations cos 2x+(1−√3)=(2−√3)cos x and sin 3x=2 sin x which satisfy the inequality √3tan x−1≥0 in [0, 5π] is
Q. Number of solutions of the equation 2(sin3θ+sin2θ)+2(cos3θ+cos2θ) = 3sin2θ
in the interval [0, 4π] is
in the interval [0, 4π] is
Q. For the given equations cos(4y−3x−2)−cos(4y+3x+2)=2+2 ln(k4−255) and cos(4y−3x−2)+cos(4y+3x+2)=2k+8 to have real solutions (x, y), the possible value of k is
- 4
- -4
- -5
- none of these
Q. If tan(πsinθ)=cot(πcosθ), then |cot(θ−π4)| is
- 1√7
- √7
- 2√7
- 2√7
Q. Consider the system of equations
xcos3y+3xcosysin2y=14
xsin3y+3xcos2ysiny=13
The value of sin2y+2cos2y is
xcos3y+3xcosysin2y=14
xsin3y+3xcos2ysiny=13
The value of sin2y+2cos2y is
- 45
- 95
- 2
- None of these