What is ( Sinx + Cosy )^2 ?

$$Sin^2x$$ + 2SinxCosy + $$Cos^2y$$

Trigonometric Identities Quiz

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| By Oxyzen28

Oxyzen28

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Quizzes Created: 1 | Total Attempts: 8,659

Questions: 10 | Attempts: 8,773 | Updated: Jun 27, 2024

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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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Questions and Answers

1.

Which of these is the identity of Sin 2x?
- A.
  
  Cos^2 x + Sin^2 x
- B.
  
  2SinxCosx
- C.
  
  SinxCosx + CosxSin x
- D.
  
  Sin^2 x
- E.
  
  Sin x + Sinx
Correct Answer
B. 2SinxCosx

Explanation
Sin 2x = Sin ( x + y )
= Sin ( x + x )
= SinxCosx + CosxSinx
= 2SinxCosx

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17
2.

Is Sec2x = 1 an identity? ( 1 - Sinx )( 1 + Sinx)
- A.
  
  True
- B.
  
  False
- C.
  
  Maybe
- D.
  
  It depends
Correct Answer
A. True
3.

True or false, Tanx + TanySecx = Tan ( x + y ) ? Cosx + TanySinx
- A.
  
  True
- B.
  
  False
- C.
  
  Maybe
- D.
  
  It depends
Correct Answer
B. 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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11
4.

Is Sin^2 x + Sin^2 ( x + y ) + 2SinxCosxSin ( x + y ) = Sin^2 y ?
- A.
  
  True
- B.
  
  False
- C.
  
  Maybe
- D.
  
  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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13
5.

What is ( Sinx + Cosy )^2 ?
- A.
  
  Sin^2x + Cos^2x
- B.
  
  1
- C.
  
  2SinxCosy
- D.
  
  SinxCosy + CosxSiny
- E.
  
  Sin^2x + 2SinxCosy + Cos^2y
Correct Answer
E. 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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13
6.

Which of the following is the correct form of the Pythagorean identity in trigonometry?
- A.
  
  Sin²x+cos²x=1
- B.
  
  Tan²x+cot²x=1
- C.
  
  Sec²x+csc²x=1
- D.
  
  Sin²x+tan²x=1
Correct Answer
A. Sin²x+cos²x=1
7.

What is Sinx + Cosx + 1 ? TanxCotx
- A.
  
  1
- B.
  
  Sinx + Cosx
- C.
  
  Cos^2 xSin^2 x
- D.
  
  2
- E.
  
  ______1________ SecxCscx
Correct Answer
B. 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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12
8.

Is 2Sec^2 xCos^2 x = 2 an identity?
- A.
  
  True
- B.
  
  False
- C.
  
  Maybe
- D.
  
  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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11
9.

Which of the following is not an identity with Cos2x?
- A.
  
  1 - Sin^2 x
- B.
  
  2Cosx - 1
- C.
  
  Cos^2 x - Sin^2 x
- D.
  
  1 - 2Sin^2 x
Correct Answer
A. 1 - Sin^2 x

Explanation
The given expression is 1 - Sin^2 x. This can be simplified using the identity Cos^2 x = 1 - Sin^2 x. By substituting this identity into the expression, we get 1 - Sin^2 x = Cos^2 x, which is an identity with Cos2x. Therefore, the correct answer is 1 - Sin^2 x, as it is not an identity with Cos2x.

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11
10.

Is Sinx + Cosx = 1 an identity?
- A.
  
  True
- B.
  
  False
- C.
  
  Maybe
- D.
  
  it depends
Correct Answer
B. False

Explanation
The equation Sinx + Cosx = 1 is not an identity because it is not true for all values of x. There are certain values of x for which the equation holds true, but there are also values for which it does not hold true. Therefore, it cannot be considered an identity.

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11

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Current Version
Jun 27, 2024

Quiz Edited by
ProProfs Editorial Team
Aug 17, 2008

Quiz Created by
Oxyzen28

Trigonometric Identities Quiz

Which of these is the identity of Sin 2x?

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

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

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

What is ( Sinx + Cosy )^2 ?

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

What is Sinx + Cosx + 1 ? TanxCotx

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

Which of the following is not an identity with Cos2x?

Is Sinx + Cosx = 1 an identity?