## MATHEMATICS TRIGONOMETRY RATIOS AND IDENTITIES QUIZ-9

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

Q1. If 1+ cos⁡x=k, where x is acute, then sin⁡x/2 is
•  √((1-k)/2)
•  √(2-k)
•  √((2+k)/2)
•  √((2-k)/2)
Solution

Q2.The equation sin⁡x+sin⁡y+sin⁡z=-3 for 0≤x≤2Ï€, 0≤y≤2Ï€, 0≤z≤2Ï€ has
•  One solution
•  Two sets of solutions
•  Four sets of solutions
•  No solution
Solution
Given equation, sinx + siny+sinz=- 3is satisfied only when x= y= z= 3Ï€/2 for x, y,z
belongs to [0,2Ï€]

Q3.  If cos⁡x=3cos⁡y, then 2 tan⁡(y-x)/2 is equal to
•  cot⁡((y-x)/2)
•  cot⁡((x+y)/4)
•  cot⁡((y-x)/4)
•  cot⁡((x+y)/2)
Solution

Q4. If tan⁡x=b/a, then the value of a cos⁡2x+b sin⁡2x is
•  1
•  b
•  ab
•  a
Solution

Q5.The value of the series cos⁡12°+cos⁡84°+cos⁡132°+cos⁡156°is
•  1/2
•  1/4
•  -1/4
•  -1/2
Solution

Q6. tan⁡9°-tan⁡27°-tan⁡63°+tan⁡81° is equal to
•   0
•   1
•  -1
•   4
Solution

Q7.The number of values of x in the interval [0,5Ï€] satisfying the equation 3 sin2x-7 sin⁡x+2=0 is
•  0
•  5
•  6
•  10
Solution

Q8.The maximum value of f(x)=sin⁡x(1+cos⁡x) is
•  (3√3)/4
•  (3√3)/2
•  3√3
•  √3
Solution

Q9.If cos⁡Î¸+cos⁡2Î¸+cos⁡3Î¸=0 , the general value of Î¸ is
•  Î¸=2nÏ€± Ï€/4
•  Î¸=nÏ€+(-1)n 2Ï€/3
•  Î¸=nÏ€+(-1)n Ï€/3
•  Î¸=2nÏ€± 2Ï€/3
Solution

Q10. If sin⁡(Î±+Î²)=1,sin⁡(Î±-Î²)=1 /2; Î±,Î²∈[0,Ï€/2], then tan⁡(Î±+2Î²) tan⁡(2Î±+Î²) is equal to
•  1
•  -1
•  0
•  1/2
Solution

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