Equations Involving sinx + cosx and sinx.cosx
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Q. Consider the system of equations
xcos3y+3xcosysin2y=14
xsin3y+3xcos2ysiny=13
The value(s) of x is/are
xcos3y+3xcosysin2y=14
xsin3y+3xcos2ysiny=13
The value(s) of x is/are
- ±5√5
- ±√5
- ±1√5
- None of these
Q. The general solution of 3tan(θ−15∘)=tan(θ+15∘) is:
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. 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. A solution of the equation log2(sinx+cosx)−log2(cosx)+1=0 in (−π4, π4) is
- tan−1(−12)
- 0
- tan−1(12)
- π6