Show thatsinθcos3θ + sin3θcos9θ

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

81.

The value of cos45°cos712°sin712° is 

  • 12

  • 18

  • 14

  • 116


82.

General solution of sinx + cosx = minaR1, a2 - 4a + 6 is

  • 2 + - 1nπ4

  • 2 + - 1nπ4

  •  + - 1n +1π4

  •  + - 1nπ4 - π4


83.

If a= 22, b = 6, A= 45°, then

  • no triangle is possible

  • one triangle is possible

  • two triangles are possible

  • either no triangle or two triangles are possible


84.

In a triangle ABC, if sinA sinB = abc2, then the triangle is

  • equilateral

  • isosceles

  • right angled

  • obtuse angled


Advertisement
85.

The value of 1 + cosπ61 + cosπ31 + cos2π31 + cos7π6 is

  • 316

  • 38

  • 34

  • 12


86.

If P = 12sin2θ + 13cos2θ then

  • 13  P  12

  • P  12

  • 2  P  3

  • - 136  P  136


87.

A positive acute angle is divided into two parts whose tangents are 12 and 13. Then, the angle is

  • π4

  • π5

  • π3

  • π6


88.

The smallest value of 5cosθ + 12 is

  • 5

  • 12

  • 7

  • 17


Advertisement

 Multiple Choice QuestionsShort Answer Type

Advertisement

89.

Show that

sinθcos3θ + sin3θcos9θ + sin9θcos27θ = 12tan27θ - tanθ


 LHS  = sinθcos3θ + sin3θcos9θ + sin9θcos27θNow, sinθcos3θ = sinθcos3θ × 2cosθ2cosθ= sin2θ2cos3θcosθ = 12sin3θ - θcos3θcosθ= 12sin3θcosθ - cos3θsinθcos3θcosθ= 12tan3θ - tanθSimilarly, sin3θcos9θ = 12tan9θ - tan3θand       sin9θcos27θ = 12tan27θ - tanθ                             = RHS


Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

90.

The equation 3sinx + cosx = 4 has

  • infinitely many solutions

  • no solution

  • two solutions

  • only one solution


Advertisement