Question

verifysin3theta=3sintheta-4sinque theta by taking theta=30°​

Answer 1

Solution:

We have to verify - sin(3x) = 3sin(x) - 4sin³(x)

Putting x = 30° in LHS, we get,

= sin(3 × 30°)

= sin(90°)

= 1 (From T-Ratio table)

Putting x = 30° in RHS, we get,

= 3 × sin(30°) - 4 × sin³(30°)

Value of sin(30°) is 1/2, therefore,

= 3 × 1/2 - 4 × (1/2)³

= 3/2 - 4/8

= 3/2 - 1/2

= 2/2

= 1

So, LHS = RHS. Hence, Verified.

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

Answer:

We have to verify - sin(3x) = 3sin(x) - 4sin³(x)

Putting x = 30° in LHS, we get,

= sin(3 × 30°)  

= sin(90°)  

= 1 (From T-Ratio table)

Putting x = 30° in RHS, we get,

= 3 × sin(30°) - 4 × sin³(30°)

Value of sin(30°) is 1/2, therefore,

= 3 × 1/2 - 4 × (1/2)³

= 3/2 - 4/8

= 3/2 - 1/2

= 2/2

= 1

So, LHS = RHS. Hence, Verified.

Step-by-step explanation:

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