Question

If x=2cos^2 ,y=2sin^2+1.find x+y

Answer 1

X+Y = 2 COS²2 + 2 SIN²2 + 1
= 2 ( COS²2+SIN²2) + 1
= 2×1 + 1
= 3

Answer 2

Answer:

The value of x+y is 3.

Step-by-step explanation:

Given that,

x = 2cos²x

y = 2sin²x + 1

We need to find the value of x+y.

→ x + y = 2cos²x + 2sin²x + 1

→ x + y = 2(cos²x + sin²x) + 1

→ x + y = 2(1) + 1

→ x + y = 2 + 1

→ x + y = 3

Hence, the value of x+y is 3.

Extra knowledge:

1. Relationship between sides and T-Ratios.

• sin(θ) = Height/Hypotenuse
• cos(θ) = Base/Hypotenuse
• tan(θ) = Height/Base
• cot(θ) = Base/Height
• sec(θ) = Hypotenuse/Base
• cosec(θ) = Hypotenuse/Height

2. Square formulae.

• sin²(θ) + cos²(θ) = 1
• 1 + tan²(θ) = sec²(θ)
• 1 + cot²(θ) = cosec²(θ)

3. Reciprocal Relationship.

• sin(θ) = 1/cosec(θ)
• cos(θ) = 1/sec(θ)
• tan(θ) = 1/cot(θ)
• cot(θ) = 1/tan(θ)
• sin(θ)/cos(θ) = 1/cot(θ)
• cos(θ)/sin(θ) = 1/tan(θ)

4. Trigonometric functions of multiple of angles.

• sin2(θ) = 2sin(θ)cos(θ)
• cos2(θ) = cos²(θ) - sin²(θ)
• cos2(θ) = 2cos²(θ) - 1
• cos2(θ) = 1 - sin²(θ)
• tan(θ) = 2tan(θ)/1 - tan²(θ)

5. Sign of Trigonometric ratios in Quadrants.

• sin (90° - θ) = cos(θ)
• cos (90° - θ) = sin(θ)
• tan (90° - θ) = cot(θ)
• csc (90° - θ) = sec(θ)
• sec (90° - θ) = csc(θ)
• cot (90° - θ) = tan(θ)
• sin (90° + θ) = cos(θ)
• cos (90° + θ) = -sin(θ)
• tan (90° + θ) = -cot(θ)
• csc (90° + θ) = sec(θ)
• sec (90° + θ) = -csc(θ)
• cot (90° + θ) = -tan(θ)
• sin (180° - θ) = sin(θ)
• cos (180° - θ) = -cos(θ)
• tan (180° - θ) = -tan(θ)
• csc (180° - θ) = csc(θ)
• sec (180° - θ) = -sec(θ)
• cot (180° - θ) = -cot(θ)
• sin (180° + θ) = -sin(θ)
• cos (180° + θ) = -cos(θ)
• tan (180° + θ) = tan(θ)
• csc (180° + θ) = -csc(θ)
• sec (180° + θ) = -sec(θ)
• cot (180° + θ) = cot(θ)
• sin (270° - θ) = -cos(θ)
• cos (270° - θ) = -sin(θ)
• tan (270° - θ) = cot(θ)
• csc (270° - θ) = -sec(θ)
• sec (270° - θ) = -csc(θ)
• cot (270° - θ) = tan(θ)
• sin (270° + θ) = -cos(θ)
• cos (270° + θ) = sin(θ)
• tan (270° + θ) = -cot(θ)
• csc (270° + θ) = -sec(θ)
• sec (270° + θ) = cos(θ)
• cot (270° + θ) = -tan(θ)