Worksheet on Establishing Conditional Results Using Trigonometric Identities

In worksheet on establishing conditional results using Trigonometric identities we will prove various types of practice questions on Trigonometric identities.

Here you will get 12 different types of establishing conditional results using Trigonometric identities questions with some selected questions hints. 

1. If sin A + cos A = 1, prove that sin A - cos A = ± 1.

2. If csc θ + cot θ = a, prove that, cos θ = a21a2+1.

3. If x cos θ + y sin θ = z, prove that

                     a sin θ + b cos θ = ± x2+y2+z2.

Worksheet on Establishing Conditional Results Using Trigonometric Identities

4. If tan2 A = 1 – e2 prove that, sec A + tan3 A csc A = (2 – e2)3/2.

5. If tan β + cot β = 2, prove that tan3 β + cot3 β =2.

6. If cos θ + sec θ = 2, prove that cos4 θ + sec4 θ =2.

Hint: cosθ - 2 cos θ + 1 = 0

     ⟹ (cos θ - 1)2 = 0

     ⟹ cos θ - 1 = 0

     ⟹ cos θ = 1

     ⟹ sec θ = 1


7. If tan2 A = 1 + 2 tan2 B, prove that cos2 B = 2 cos2 A

Hint: tan2 A = 1 + 2 tan2 B

     ⟹  sec2 A - 1 = 1 + 2 (sec2 B - 1)

     ⟹  sec2 A - 1 = 1 + 2 sec2 B - 2

     ⟹  sec2 A - 1 = 2 sec2 B - 1


8. If cos A + sec A = 3 show that, cos3 A + sec3 A = 0.

9. If cos2 A – sin2 A = tan2 B, prove that tan2 A = cos2 B – sin2 B.

Hint: cos2 A – sin2 A = tan2 B

     ⟹  cos2 A – (1 - cos2 A) = sec2 B - 1

     ⟹  cos2 A – 1 + cos2 A = sec2 B - 1

     ⟹  2 cos2 A – 1 = sec2 B - 1

     ⟹  2 cos2 A = sec2 B 

     ⟹  2 1sec2A 1cos2B 

     ⟹  sec2 A = 2 cos2 B 

     ⟹  1 + tan2 A = cos2 B + cos2 B 

     ⟹  tan2 A = cos2 B + cos2 B - 1

     ⟹  tan2 A = cos2 B - 1 + cos2 B

     ⟹  tan2 A = cos2 B - (1 - cos2 B)


10. If a2 sec2  θ – b2 tan2 θ = c2, show that sin θ = ±c2a2c2b2.

11. If (1 – cos A)(1 – cos B)(1 – cos C) = (1 + cos A)(1 + cos B)(1 + cos C) then prove that each side is equal to ± sin A sin B sin C.

12. If 4x sec β = 1 + 4x2, prove that, sec β + tan β = 2x or, 12x.





10th Grade Math

From Worksheet on Establishing Conditional Results Using Trigonometric Identities to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More