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# Trigonometry- MCQ Test 2

### 1. If x = a cos 0 and y = b sin 0, then b²x² + a²y²=?

given, x = a cos 0 and y = b sin 0
Putting sin 0=0,cos 0 =1 => x=a, y=0
b²x² + a²y² => b²a²

### 2. If secθ+tanθ=x, then secθ is :

Given, secθ+tanθ=x..... eqn (1)
As we know that
sec²θ−tan²θ=1
⟹(secθ−tanθ)(secθ+tanθ)=1
⟹(secθ−tanθ)=1/(secθ+tanθ)
⟹(secθ−tanθ)=1/x ..... eqn(2)
Adding eqn (1) and eqn(2)weget
2secθ=x+1/x=(x²+1)/2x
secθ=(x²+1)/2x

### 3.If secθ+tanθ=x, then tanθ is :

Given, secθ+tanθ=x..... eqn (1)
As we know that
sec²θ−tan²θ=1
⟹(secθ−tanθ)(secθ+tanθ)=1
⟹(secθ−tanθ)=1/(secθ+tanθ)
⟹(secθ−tanθ)=1/x ..... eqn(2)
Substracting eqn (2) from eqn(1)weget
2tanθ=x-1/x=(x²-1)/2x
tanθ=(x²-1)/2x

### 4. If (1-cos x)/sinx = ?

(1-cos x)/sinx
Multiplaying (1+cos x) in numarator and denumarator weget
(1-cos x)(1+cos X)/sinA(1+cos x)
(1-cos² x)/sinx(1+cos x)
(sin² x)/sinx(1+cos x)

cos 90°=0

### 7. Given that sin θ = x/y , then tan θ =

Explanation/Answer:- cos² θ=1-sin² θ=>cos θ= √1-(x/y)²
tan θ=sin θ/cos θ=x/√y²-x²

### 8. If sin A – cos A = 0, then the value of sin^4 A + cos^4 A is

Explanation/Answer:- Given,sin A – cos A = 0
=>sin A = cos A
=> tanA = 1
=> A=45°
sin^4 A + cos^4 A={(1/√2)²}²+{(1/√2)²}²
=>{(1/4)+{(1/4)}=1/2

### 9. If cos 9A = sin A and 9A < 90°, then the value of tan 5A is

⇒ cos 9A = sin A ⇒cos 9A = cos(90- A)
⇒ 9A = 90° - A
⇒ 10 A = 90°
⇒ A = = 9°
∴ 5A = 5 × 9° = 45°
⇒ tan45°=1