Question

if x is equal to cos theta and Y equal to b sin theta then find the value of B Square X square + Y square​

Answer 1

Question

If x is equal to cos theta and y is equal to b sin theta then find the value of b²x² + y².

Answer

b²x² + y² = b²

Solution

Given that, x = cosØ and y = b sin ØWe have to find the value of b²x² + y²

Just simply put the known values.

→ b²x² + y²

→ b²(cos Ø)² + (b sin Ø)²

→ b² cos²Ø + b² sin²Ø

Take b² as common

→ b²(cos²Ø + sin²Ø)

→ b²(1)

→ b²

Used identity is cos²Ø + sin²Ø = 1

Trigonometry formulas

→ sinØ = cos(90° - Ø)

→ secØ = cosec(90° - Ø)

→ tanØ = cot(90° - Ø)

→ sinØ = 1/cosecØ

→ secØ = 1/cosØ

→ tanØ = 1/cotØ

→ sin²Ø + cos²Ø = 1

→ 1 + tan²Ø = sec²Ø

→ 1 + cot²Ø = cosec²Ø

Answer 2

Given :--

• x = cosθ
• y = bsinθ

To Find :--

• (b²x² + y²)

Solution :---

we have to Find value of (b²*x² + y²) ,,Let try to put values ,

→ (b²*x² + y²)

Putting values from given,

→ (b²) * (cosθ)² + (bsinθ)²

→ (b²*cos²θ) + (b²*sin²θ)

Taking b² common now,

→ b²(cos²θ + sin²θ)

Now, we know that, cos²θ + sin²θ = 1.

So,

→ b²(cos²θ + sin²θ)

→ b² * 1

→ b² (Ans).