Question

given statement cos tita + cos^tita = 1,then sin^2 tita +sin^4tita=1 true or false ​

Answer 1

Answer:

• True.

Explanation:

It's given that,

→ cos(x) + cos²(x) = 1

→ cos(x) = 1 - cos²(x)

As we know that,

→ sin²(x) + cos²(x) = 1

So,

→ sin²(x) = 1 - cos²(x)

Therefore,

→ cos(x) = sin²(x)

Also,

→ cos²(x) = (sin²(x))² = sin⁴(x)

So,

sin²(x) + sin⁴(x)

= sin²(x) + cos²(x)

= 1 [As sin²(x) + cos²(x) = 1]

∆ So, this equality holds true.

Learn More:

1. Relationship between sides.

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

2. Square formulae.

• sin²x + cos²x = 1.
• cosec²x - cot²x = 1.
• sec²x - tan²x = 1

3. Reciprocal Relationship.

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

4. Cofunction identities.

• sin(90° - x) = cos(x) and vice versa.
• cosec(90° - x) = sec(x) and vice versa.
• tan(90° - x) = cot(x) and vice versa.

Answer 2

Step-by-step explanation:

Answer:

True.

Explanation:

It's given that,

→ cos(x) + cos²(x) = 1

→ cos(x) = 1 - cos²(x)

As we know that,

→ sin²(x) + cos²(x) = 1

So,

→ sin²(x) = 1 - cos²(x)

Therefore,

→ cos(x) = sin²(x)

Also,

→ cos²(x) = (sin²(x))² = sin⁴(x)

So,

sin²(x) + sin⁴(x)

= sin²(x) + cos²(x)

= 1 [As sin²(x) + cos²(x) = 1]

• ∆ So, this equality holds true.

Learn More:

• 1. Relationship between sides.

sin(x) = Height/Hypotenuse.

cos(x) = Base/Hypotenuse.

tan(x) = Height/Base.

cot(x) = Base/Height.

sec(x) = Hypotenuse/Base.

cosec(x) = Hypotenuse/Height.

• 2. Square formulae.

sin²x + cos²x = 1.

cosec²x - cot²x = 1.

sec²x - tan²x = 1

• 3. Reciprocal Relationship.

sin(x) = 1/cosec(x).

cos(x) = 1/sec(x).

tan(x) = 1/cot(x).

• 4. Cofunction identities.

sin(90° - x) = cos(x) and vice versa.

cosec(90° - x) = sec(x) and vice versa.

tan(90° - x) = cot(x) and vice versa.

hope this helps you!!