Trigonometry — TN TET Mathematics Questions

5 free practice questions on Trigonometry, out of 29 in this topic, for Tamil Nadu Teacher Eligibility Test (TN TET) aspirants. Each one shows the correct answer and a full explanation.

Q1Easy

sin²θ + cos²θ = ?

  1. a0
  2. b1✓ Correct
  3. c2
  4. d-1

Explanation

This is the fundamental Pythagorean trigonometric identity: sin²θ + cos²θ = 1.

இது அடிப்படை பித்தகோரியன் முக்கோணவியல் சர்வசமன்பாடு: sin²θ + cos²θ = 1.

Q2Easy

The value of sin 30° is?

sin 30° இன் மதிப்பு என்ன?

  1. a1
  2. b1/2✓ Correct
  3. c0
  4. d√3/2

Explanation

sin 30° = 1/2. Standard values: sin 0°=0, sin 30°=1/2, sin 45°=1/√2, sin 60°=√3/2, sin 90°=1.

sin 30° = 1/2. நிலையான மதிப்புகள்: sin 0°=0, sin 30°=1/2, sin 45°=1/√2, sin 60°=√3/2, sin 90°=1.

Q3Easy

tan 45° = ?

  1. a√3
  2. b1/√3
  3. c0
  4. d1✓ Correct

Explanation

tan 45° = sin 45°/cos 45° = (1/√2)/(1/√2) = 1.

Q4Easy

Value of sin²30° + cos²60°:

பாவத்தின் மதிப்பு²30° + cos²60°:

  1. a1/2✓ Correct
  2. b1
  3. c0
  4. d√3/2

Explanation

(1/2)² + (1/2)² = 1/4+1/4 = 1/2.

Q5Easy

(1+tanθ)² + (1+cotθ)² = ?

  1. a2
  2. bsec²θ+cosec²θ
  3. c(secθ+cosecθ)²✓ Correct
  4. dsin²θ+cos²θ

Explanation

(1+t)²+(1+c)² = 1+2t+t²+1+2c+c² = 2+2(t+c)+sec²θ+cosec²θ. And (secθ+cosecθ)² = sec²+cosec²+2secθcosecθ. Let's verify: (1+tanθ)² = sec²θ+2tanθ, (1+cotθ)²=cosec²θ+2cotθ. Sum = sec²+cosec²+2(tanθ+cotθ) = sec²+cosec²+2(sinθ/cosθ+cosθ/sinθ) = sec²+cosec²+2/sinθcosθ = sec²+cosec²+2secθcosecθ = (secθ+cosecθ)².

(1+t)²+(1+c)² = 1+2t+t²+1+2c+c² = 2+2(t+c)+sec²θ+cosec²θ. மற்றும் (secθ+cosecθ)² = sec²+cosec²+2secθcosecθ. சரிபார்ப்போம்: (1+tanθ)² = sec²θ+2tanθ, (1+cotθ)²=cosec²θ+2cotθ. தொகை = sec²+cosec²+2(tanθ+cotθ) = sec²+cosec²+2(sinθ/cosθ+cosθ/sinθ) = sec²+cosec²+2/sinθcosθ = sec²+cosec¸= (secθ+cosecθ)².

24 more questions on Trigonometry

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