# Mathematics Questions and Answers – Trigonometric Identities – 1

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Trigonometric Identities – 1”.

1. An identity is an equation.
a) False
b) True

Explanation: Yes, an equation is an identity. If this identity is true for all values of the variables in an equation. For example (a – b)2 = a2 + b2 – 2ab is an identity.

2. Find the correct trigonometric identity.
a) tan2θ = sec2θ – 1
b) tan2θ + sec2θ = 1
c) tan2θ – sec2θ = 1
d) tan2θ = sec2θ + 1

Explanation: The appropriate trigonometric identity used here is sec2θ – tan2θ = 1.
-tan2θ = 1 – sec2θ
tan2θ = sec2θ – 1

3. Evaluate (cosec θ – cot θ) (cosec θ – cot θ).
a) 0
b) 1
c) 2
d) 3

Explanation: (cosec θ – cot θ) (cosec θ – cot θ) = cosec2θ – cot2θ
= 1
The identity used here is cosec2θ – cot2θ = 1

4. Evaluate cosec θ sec θ.
a) cos θ + tan θ
b) cos θ – tan θ
c) tan θ – cot θ
d) cot θ + tan θ

Explanation: cosec θ sec θ = $$\frac {1}{sin \, \theta } \frac {1}{cos \, \theta }$$
= $$\frac {1}{sin \, \theta \, cos \, \theta }$$(cos2θ + sin2θ)
= $$\frac {cos \, \theta }{sin \, \theta } + \frac {sin \, \theta }{cos \, \theta }$$
= cot θ + tan θ

5. Evaluate $$\frac {1+cos \, \theta }{sin \, \theta }$$(cosec θ – cot θ).
a) cosec θ + cot θ
b) cot2 θ + tan2 θ
c) cot θ – tan θ
d) cosec2 θ – cot2 θ

Explanation: $$\frac {1+cos \, \theta }{sin \, \theta }$$(cosec θ – cot θ) = $$\frac {1}{sin \, \theta }+ \frac {cos \, \theta }{sin \, \theta }$$(cosec θ – cot θ)
= (cosec θ + cot θ)(cosec θ – cot θ)
= cosec2 θ – cot2 θ

6. Sec2 θ – Sec4 θ equals to _____
a) –Sec2 θ Tan2 θ
b) – Sec2 θ Tan2 θ
c) 1
d) 0

Explanation: Sec2 θ – Sec4 θ = Sec2 θ (1 – Sec2 θ) (∵ sec2 θ – tan2 θ = 1)
= Sec2 θ (-Tan2 θ)
= -Sec2 θ Tan2 θ

7. Find the distance between (sin θ, 0) and (0, cos θ).
a) 0
b) 1
c) $$\frac {4}{3}$$
d) $$\frac {3}{4}$$

Explanation: Let (x1, y1) = (sin θ, 0) and (x2, y2) = (0, cos θ)
Distance between two points = √((x2 – x1)2 + (y2 – y1)2)
= √((0 – sin θ)2 + (cos θ – 0)2)
= √(sin2 θ + cos2 θ)
= √1
= 1

8. (sin A – cos A)2 is equal to _____
a) 1 + 2sin A cos A
b) 1 – 2sin A cos A
c) 2sin A cos A – 1
d) 2sin A cos A + 1

Explanation: (sin A – cos A)2 = sin2 A + cos2 A – 2sin A cos A
= 1 – 2sin A cos A

9. Evaluate sec2 A + (1 + tan A) (1 – tan A).
a) 3
b) 0
c) 2
d) 1

Explanation: sec2 A + (1 + tan A) (1 – tan A) = sec2 A + 12 – tan2 A
= (sec2 A – tan2 A) + 1
= 1 + 1
= 2

10. Sec θ – $$\frac {1}{sec \, \theta }$$ is _____
a) Tan θ / Sec ⁡θ
b) Tan2 θ / Sec ⁡θ
c) Tan θ / Sec2 ⁡θ
d) Sec⁡ θ / Tan ⁡θ

Explanation: Sec θ – $$\frac {1}{sec \, \theta } = \frac {1}{sec \, \theta }$$(Sec2 θ – 1)
= $$\frac {1}{sec \, \theta }$$(Tan2 θ)
= Tan2 θ / Sec ⁡θ

Sanfoundry Global Education & Learning Series – Mathematics – Class 10.

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