TS EAMCET · Maths · Trigonometric Equations
If \(a, b\) are real numbers and \(\alpha\) is a real root of \(x^2+12+3 \sin (a+b x)+6 x=0\) then the value of \(\cos (a+b \alpha)\) for the least positive value of \(a+b \alpha\) is
- A -1
- B \(\frac{1}{\sqrt{2}}\)
- C \(\frac{1}{2}\)
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
\((x+3)^2 + 3(1 + \sin (a+b x)) = 0\) Since \((x+3)^2 \ge 0\) and \(1+\sin (a+b x) \ge 0\), then \((x+3)^2 = 0\) and \(1+\sin (a+b x) = 0\). \(x = -3 \implies \alpha = -3\) \(\sin (a+b x) = -1\) \(\sin (a+b\alpha) = -1\) The least positive value for \(a+b\alpha\) is…
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
- The incentre of the triangle with vertices and is:TS EAMCET 2021 Easy
- The locus of the point \(P(\mathbf{r})\) which encloses a triangle \(A B P\) of area l sq. unit with the fixed points \(A(\hat{\mathbf{i}})\) and \(B(\hat{\mathbf{j}})\) isTS EAMCET 2020 Easy
- When \(a\) is irrational, the number of solutions satisfying the equation \(1+\sin ^2 a x=\cos x\) isTS EAMCET 2018 Easy
- \(\int \frac{2 x+2}{\sqrt{x^2-4 x-5}} d x\) is equal toTS EAMCET 2016 Medium
- The cartesian form of the polar equation \(\theta=\tan ^{-1} 2\) isTS EAMCET 2005 Easy
- In any triangle \(A B C\), if \(a: b: c=2: 3: 4\), then \(R: r=\)TS EAMCET 2019 Medium
More PYQs from TS EAMCET
- \(\left(x^4+1\right)=\frac{1}{a}(x+1)^4\) is a reciprocal equationTS EAMCET 2022 Medium
- If the origin of a coordinate system is shifted to \((-\sqrt{2}, \sqrt{2})\) and the coordinate system is rotated anti-clockwise through an angle \(45^{\circ}\), then the point \(P(1,-1)\) in the original system has new coordinatesTS EAMCET 2015 Easy
- If the radical axis of the circles \(x^2+y^2+2 \alpha x+2 \beta y+c=0\) and \(x^2+y^2+\frac{3}{2} x+4 y+c=0\) touches the circle \(x^2+y^2+2 x+2 y+1=0\), then \(4 \alpha \beta-8 \alpha-3 \beta+10=\)TS EAMCET 2020 Hard
- A student is asked to answer 10 out of 13 questions is an examination such that he must answer atleast four questions from the first five questions. The number of choices available to him isTS EAMCET 2019 Easy
- If \(1-i\) is a root of the equation \(x^2+a x+b=0\) then \(b\) is equal toTS EAMCET 2002 Easy
- The coordinates of the point \(P\) on the curve \(x=a(\theta+\sin \theta), y=a(1-\cos \theta)\), where the tangent is inclined at an angle \(\frac{\pi}{4}\) to \(x\)-axis, areTS EAMCET 2012 Easy