AP EAMCET · Maths · Trigonometric Equations
If \(\sin \theta+2 \cos \theta=1\) and \(\theta\) belongs to \(4^{\text {th }}\) quadrant (not lying on the coordinate axes) then \(7 \cos \theta+6 \sin \theta=\)
- A \(\frac{4}{17}\)
- B \(2\)
- C \(\frac{7}{17}\)
- D \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\( \sin \theta = 1 - 2 \cos \theta \) \( (1 - 2 \cos \theta)^2 + \cos^2 \theta = 1 \) \( 1 - 4 \cos \theta + 4 \cos^2 \theta + \cos^2 \theta = 1 \) \( 5 \cos^2 \theta - 4 \cos \theta = 0 \) \( \cos \theta (5 \cos \theta - 4) = 0 \) \( \cos \theta = \frac{4}{5} \) (since…
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 number of solutions for \(z^3+\bar{z}=0\), isAP EAMCET 2014 Easy
- If \(\alpha, \beta, \gamma\) are the roots of \(x^3+p x^2+q x+r=0\), then the value of \(\left(1+\alpha^2\right)\left(1+\beta^2\right)\left(1+\gamma^2\right)\) isAP EAMCET 2017 Medium
- If the function , where , attains its maximum and minimum at and respectively such that , then equalsAP EAMCET 2021 Hard
- 2 aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if first misses the target. The probability that the target is hit by the 2 nd plane isAP EAMCET 2021 Easy
- Let \(P(\alpha, \beta)\) and \(Q(\gamma, \delta)\) be two points that lie on the curve \(\tan ^2(x+y)+\cos ^2(x+y)\) \(+y^2+2 y=0\) in the \(X Y\)-plane. If the distance between \(P\) and \(Q\) is \(d\), then \(\cos d=\)AP EAMCET 2018 Medium
- The general solution of the differential equation \((x-(x+y) \log (x+y)) d x+x d y=0\) isAP EAMCET 2025 Medium
More PYQs from AP EAMCET
- Two spheres ' \(A\) ' and ' \(B\) ' of equal mass lie at rest at the opposite ends of a diameter of a smooth horizontal circular groove of radius ' \(r\) '. 'A' moves and collides with ' \(B\) ' after a time ' \(t\) '. If ' \(e\) ' is the coefficient of restitution, next collision between the spheres takes place after a time of ____AP EAMCET 2017 Medium
- The straight line passing through \((-1,1)\) and remaining parallel to the line common to the pairs of lines provided by \(6 x^2-x y-12 y^2=0\) and \(15 x^2+14 x y-8 y^2=0\), isAP EAMCET 2022 Medium
- The equilibrium concentrations of \(\mathrm{N}_2, \mathrm{H}_2\) and \(\mathrm{NH}_3\) in the formation of \(\mathrm{NH}_3\) at \(500 \mathrm{~K}\) are \(1.25 \times 10^{-2} \mathrm{M}, 4.0 \times 10^{-2} \mathrm{M}\) and \(1.6 \times 10^{-2} \mathrm{M}\) respectively. The equilibrium constant \(\mathrm{K}_{\mathrm{p}}\) at the same temperature isAP EAMCET 2018 Easy
- Sea divers use a mixture ofAP EAMCET 2015 Easy
- BOD meansAP EAMCET 2020 Easy
- The values of a function \(f(x)\) at different values of \(x\) are as follows
Then, the approximate area (in square units) bounded by the curve \(y=f(x)\) and \(x\)-axis between \(x=0\) and 5 , using the Trapezoidal rule, isAP EAMCET 2010 Hard