Introduction To Trigonometry - Free MCQ Practice Test with solutions,

sin 30° = 1/2,
cos 30°=√3/2,
sin 60°=√3/2,
cos 60°=1/2,
By putting the value of sin 30°, cos 30°, sin 60° and cos 60° in equation

We get=
(sin30°+cos30°)-(sin60°+cos60°)=(1/2+√3/2)-(√3/2+1/2)
=0

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

sin 45° + cos 45°
We know that:
sin 45° = 1/√2
cos 45° = 1/√2
Hence, the answer is = √2

Substitute these values

(sin 45° + cos 45°)
= (1/√2) + (1/√2)

Add the fractions

Both fractions have the same denominator, so we add the numerators:
(1 + 1) / √2 = 2 / √2

Simplify the fraction

Divide numerator and denominator by √2:
(2 / √2) = (2 × √2) / 2 = √2

Final Answer: (sin 45° + cos 45°) = √2

Let,angle= θ
(asinθ + bcosθ)/(asinθ - bcosθ)
Dividing both numerator and denominator from cosθ
We get,
atanθ +b/atanθ - b
= ( a.a/b + b) /(a.a/b - b) =(a²/b +b)/(a²/b - b)
=(a² + b²/a²- b²) 

6cot+2cosec=cot+5cosec
6cot-cot=5cosec-2cosec
5cot=3cosec
5cos/sin=3/sin
cos=3/5

Correct Answer :- B
1–B, 2–C, 3–A

9 sec² A - 9 tan² A
= 9( sec² A - tan² A)
= 9 × 1
= 9

Solution:

We know, sin 30° = 1/2 and cos 30° = √3/2.

Therefore, sin² 30° - cos² 30° = (1/2)² - (√3/2)²

= 1/4 - 3/4 = -2/4

= -1/2

Tanθ = Perpendicular / Base
We are given that TanA = 3/2
On comparing
Perpendicular = 3
Base = 2
To fing hypotenuse
Hypotenuse² = Perpendicular² + Base²
Hypotenuse² = 3² + 2²
Hypotenuse = 
Hypotenuse = 3.6

Cosθ = Base / Hypotenuse
CosA = 2 / 3.6
Hence the value of Cos A is 2/3.6=2/√13

3 cot θ = 2 ⇒ cot θ = 2/3 ⇒ tan θ = 3/2