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 = \(\frac{a^{2} - 1}{ a^{2} + 1}\).

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

                     a sin θ + b cos θ = ± \(\sqrt{x^{2} + y^{2} + z^{2} }\).

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 = \(\sqrt{3}\) 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 \(\frac{1}{sec^{2} A}\) \(\frac{1}{cos^{2} B}\) 

     ⟹  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 = ±\(\sqrt{\frac{c^{2} – a^{2}}{c^{2} – b^{2}}}\).

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, \(\frac{1}{2x}\).





10th Grade Math

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


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.



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.



Share this page: What’s this?

Recent Articles

  1. Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

    Dec 04, 23 02:14 PM

    Different types of Indian Coins
    Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes:

    Read More

  2. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 04, 23 01:50 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  3. The Story about Seasons | Spring | Summer | Autumn | Winter

    Dec 04, 23 01:49 PM

    The Four Seasons
    Kids let’s enjoy the story about seasons. Here we will discuss about the four seasons and the duration. Some months are too hot and some are too cold. The period of hot months is called the hot

    Read More