Question

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Answer 1

Solution:

Given That:

→ 4 sin θ = 3

→ sin θ = 3/4

Now, we have:

= 4 sin²θ - 3 cos²θ + 2

Can be written as:

= 4 sin²θ - 3(1 - sin²θ) + 2 [As sin²θ + cos²θ = 1]

= 4 sin²θ - 3 + 3 sin²θ + 2

= 7 sin²θ - 1

= 7 × 9/16 - 1

= 63/16 - 1

= (63 - 16)/16

= 47/16

Therefore:

→ 4 sin²θ - 3 cos²θ + 2 = 47/16 (Answer)

Learn More:

1. Relationship between sides and T-Ratios.

• 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.

• sin²(x) + cos²(x) = 1
• cosec²(x) - cot²(x) = 1
• sec²(x) - tan²(x) = 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)
• cos(90° - x) = sin(x)
• cosec(90° - x) = sec(x)
• sec(90° - x) = cosec(x)
• tan(90° - x) = cot(x)
• cot(90° - x) = tan(x)

5. Even odd identities.

• sin(-x) = -sin(x)
• cos(-x) = cos(x)
• tan(-x) = -tan(x)