TS EAMCET · Maths · Trigonometric Equations
The set of solutions of the equation \((\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2\) is
- A \(\left\{2 n \pi \pm \frac{\pi}{4}+\frac{\pi}{12}: n \in Z\right\}\)
- B \(\left\{2 n \pi \pm \frac{\pi}{4}-\frac{\pi}{12}: n \in Z\right\}\)
- C \(\left\{n \pi+(-1)^n \frac{\pi}{4}+\frac{\pi}{12}: n \in Z\right\}\)
- D \(\left\{n \pi+(-1)^n \frac{\pi}{4}-\frac{\pi}{12}: n \in Z\right\}\)
Answer & Solution
Correct Answer
(A) \(\left\{2 n \pi \pm \frac{\pi}{4}+\frac{\pi}{12}: n \in Z\right\}\)
Step-by-step Solution
Detailed explanation
\((\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2\) \(\frac{\sqrt{3}-1}{2} \sin \theta+\frac{\sqrt{3}+1}{2} \cos \theta=1\) ...(i) Comparing with \(a \sin \theta+b \cos \theta=1\). ie, \(\quad a=\frac{\sqrt{3}-1}{2}, b=\frac{\sqrt{3}+1}{2}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(b>a)\) is an ellipse with eccentricity \(\frac{1}{\sqrt{2}}\). If the angle of intersection between the ellipse and parabola \(y^2=4 a x\) is \(\theta\), then the coordinates of the point \(\frac{2 \theta}{3}\) on the ellipse isTS EAMCET 2025 Hard
- The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines \(x=0\) and \(y=0\) isTS EAMCET 2007 Medium
- In a discrete data \(\frac{\text { lth }}{4}\) of the observations are equal to \(a\), another \(\frac{\text { th }}{4}\) of the observations are equal to \(-a\). Out of the remaining, half of them are equal to \(b\) and the rest are equal to \(-b\). If the variance of all the observations is \((a b)\), thenTS EAMCET 2020 Medium
- Statement (I) : The range of the ungrouped data does not change even if certain intermediate observations are removed. Statement (II) : The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value of the mean deviation computed about any other measure of central tendency. Statement (III) : For a grouped data, range is approximated as the difference between the lower limit of the largest class and the upper limit of the smallest class.TS EAMCET 2022 Medium
- if \(3^{2 n+2}-8 n-9\) is divisible by \(2^p \forall n \in N\), then the maximum value of \(p\) isTS EAMCET 2024 Easy
- The cubic equation whose roots are thrice to each of the roots of \(x^3+2 x^2-4 x+1=0\) isTS EAMCET 2008 Medium
More PYQs from TS EAMCET
- If \(y=\frac{a x+b}{c x+d}\), than \(\frac{d x}{d y}=\)TS EAMCET 2022 Easy
- On a temperature scale \(Y\), water freezes at \(-160^{\circ} Y\) and boils at \(-50^{\circ} Y\). On this \(Y\) scale, a temperature of \(340 \mathrm{~K}\) isTS EAMCET 2013 Easy
- The possible final products and of the following reaction sequence are
TS EAMCET 2021 Hard - grams of a gas at and pressure occupies a volume of . The gas can beTS EAMCET 2020 Easy
- The area of the region bounded by the curves \(y=9 x^2\) and \(y=5 x^2+4\) (in sq units) isTS EAMCET 2015 Easy
- The equation to the line joining the centres of the circles belonging to the coaxial system of circles \(4 x^2+4 y^2-12 x+6 y-3+\lambda(x+2 y-6)=0\) isTS EAMCET 2012 Medium