Trigonometric Ratios of Multiple of an Angle
Trending Questions
Q. The number of solutions of the equation 32tan2x+32sec2x=81, 0≤x≤π4 is
- 3
- 1
- 2
- 0
Q. The set of value(s) of a for which x2+ax+sin−1(x2−4x+5)+cos−1(x2−4x+5)=0 has at least one solution is
Q. Let S be the set of all α∈R such that the equation, cos2x+αsinx=2α−7 has a solution. Then S is equal to:
- R
- [2, 6]
- [1, 4]
- [3, 7]
Q. The solution set of the equation 2sin2x+√3cosx+1=0 is {2nπ±aπb, n∈Z; ab∈[0, 1]} where a, b are co-prime. Then the value of a+b is
- 10
- 11
- 9
- 15
Q. Let 0≤x, y, z≤π2 such that sinx⋅siny⋅cosz=14√2, sin2x⋅sin3ycosz=14√2 and sinx⋅sin4ycos2z=18, then which of the following is/are correct?
- sinx+siny=32
- cos(x−y)=√32
- tan(x+y+z)=√3−2
- sec(y−z)=√6−√2
Q. If the sum of the solutions of the equation cos(π3−θ)cos(π3+θ)−secθ4=0 in [0, 10π] is kπ, then the value of k is
Q.
If y(x) is a solution of (2+sinx1+y)dydx=−cosx and y(0)=1, then find the value of y(π2).
Q. For x∈(0, π), the equation sinx+2sin2x−sin3x=3 has
- no solution
- one solution
- two solutions
- three solutions
Q. Total number of solutions for the equation sin4x+cos4x=sinxcosx , x∈[0, 2π] is
- 4
- 2
- 6
- 3
Q. The number of common solution(s) of the trigonometric equations cos2x+(1−√3)=(2−√3)cosx and sin3x=2sinx, satisfying the inequality √3tanx−1≥0 in [0, 5π] is
Q. The number of solutions of the equation sin−1[x2+13]+cos−1[x2−23]=x2, for x∈[−1, 1] and [x] denotes the greatest integer less than or equal to x, is
- 0
- 2
- 4
- Infinite
Q.
The complex number sin x+i cos 2x and cos x - i sin 2x are conjugate to each other for :