Trigonometric Identities Quiz

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  • 1/10 Questions

    Is Sinx + Cosx  = 1 an identity?

    • True
    • False
    • Maybe
    • It depends
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About This Quiz

Trigonometry is one of the core branches of Mathematics dealing with angles and calculations. This Trigonometric Identities quiz will gauge your understanding of the complex and interesting topic. Once you master Trignometry, you no longer fear Maths. This quiz has comprehensive coverage of easy, medium, to hard-level questions. So let's see how prepared you are to attempt these questions. If you find the quiz helpful, do share it with your friends. All the best!
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Trigonometric Identities Quiz - Quiz

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  • 2. 

    Which of these is the identity of Sin 2x?

    • Cos^2 x + Sin^2 x

    • 2SinxCosx

    • SinxCosx + CosxSin x

    • Sin^2 x

    • Sin x + Sinx

    Correct Answer
    A. 2SinxCosx
    Explanation
    Sin 2x = Sin ( x + y )
    = Sin ( x + x )
    = SinxCosx + CosxSinx
    = 2SinxCosx

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  • 3. 

    True or false, Tanx   +          TanySecx         =  Tan ( x + y ) ?                                    Cosx + TanySinx

    • True

    • False

    • Maybe

    • It depends

    Correct Answer
    A. False
    Explanation
    The given equation is "Tanx + TanySecx = Tan(x + y)". However, the correct equation should be "Tanx + TanySecx = Tan(x + y) + Cosx + TanySinx". Therefore, the answer is false.

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  • 4. 

    What is ( Sinx + Cosy )^2 ?

    • Sin^2x + Cos^2x

    • 1

    • 2SinxCosy

    • SinxCosy + CosxSiny

    • Sin^2x + 2SinxCosy + Cos^2y

    Correct Answer
    A. Sin^2x + 2SinxCosy + Cos^2y
    Explanation
    The given expression is (Sin x + Cos y)^2. When we expand this expression, we get Sin^2 x + 2Sin x Cos y + Cos^2 y. Therefore, the correct answer is Sin^2 x + 2Sin x Cos y + Cos^2 y.

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  • 5. 

    Is 2Sec^2 xCos^2 x = 2 an identity?

    • True

    • False

    • Maybe

    • It depends

    Correct Answer
    A. True
    Explanation
    The given expression, 2Sec^2 xCos^2 x, simplifies to 2, which is a constant value regardless of the value of x. Therefore, the expression is an identity, meaning it holds true for all values of x.

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  • 6. 

    Is Sec2x =                1               an identity?                 ( 1 - Sinx )( 1 + Sinx)  

    • True

    • False

    • Maybe

    • It depends

    Correct Answer
    A. True
  • 7. 

    What is Sinx + Cosx +             1              ?                                        TanxCotx

    • 1

    • Sinx + Cosx

    • Cos^2 xSin^2 x

    • 2

    • ______1________ SecxCscx

    Correct Answer
    A. Sinx + Cosx
    Explanation
    The given expression is Sinx + Cosx. This is the correct answer because it matches with the expression provided in the question.

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  • 8. 

    Is Sin^2 x + Sin^2 ( x + y ) + 2SinxCosxSin ( x + y ) = Sin^2 y ?

    • True

    • False

    • Maybe

    • It depends

    Correct Answer
    A. True
    Explanation
    The given equation is true. This can be proven by using the trigonometric identity: Sin^2(x) + Cos^2(x) = 1. By substituting Sin^2(x) with (1 - Cos^2(x)) in the equation, we can simplify it to: (1 - Cos^2(x)) + Sin^2(x + y) + 2Sin(x)Cos(x)Sin(x + y) = Sin^2(y). Simplifying further, we get: 1 + Sin^2(x + y) + 2Sin(x)Cos(x)Sin(x + y) = Sin^2(y). Since 1 + Sin^2(x + y) is equal to Sin^2(y) according to the trigonometric identity, the equation is true.

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  • 9. 

    Which of the following is not an identity with Cos2x?

    • 1 - Sin^2 x

    • 2Cosx - 1

    • Cos^2 x - Sin^2 x

    • 1 - 2Sin^2 x

    Correct Answer
    A. 1 - Sin^2 x
    Explanation
    The formula cos(2x) = cos²x − sin²x is the double-angle identity derived from the basic cosine addition formula:
    cos(a + b) = cos a cos b − sin a sin b
    So setting a = b = x gives:
    cos(2x) = cos²x − sin²x
    From this, using the Pythagorean identity sin²x = 1 − cos²x, or vice versa, you derive the other two forms:
    cos(2x) = 2cos²x − 1
    cos(2x) = 1 − 2sin²x
    But 2sinx cosx = sin(2x), which belongs to sine double angle, not cosine. Hence, it's not a valid identity for cos(2x).

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  • 10. 

    Which of the following is the correct form of the Pythagorean identity in trigonometry?

    • Sin2x+cos2x=1

    • Tan2x+cot2x=1

    • Sec2x+csc2x=1

    • Sin2x+tan2x=1

    Correct Answer
    A. Sin2x+cos2x=1

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  • Current Version
  • Jul 08, 2025
    Quiz Edited by
    ProProfs Editorial Team
  • Aug 17, 2008
    Quiz Created by
    Oxyzen28
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