Answered

IDNLearn.com offers a comprehensive platform for finding and sharing knowledge. Ask your questions and get detailed, reliable answers from our community of experienced experts.

If 3sin ⁻¹ (2x/1+x²)-4cos⁻¹(1–x²/1+x²)+2tan⁻¹(2x/1–x²)=π/3. Then, x=.

a 1/√3 b1/√2 c 2 d 1​

Sagot :

TheUnknownScientistidn

Answer:

Option A.)

The answer is 1/√3

Step-by-step explanation:

3sin⁻¹ (2x/1 + x²) - 4cos⁻¹ (1 - x²/1 + x²) + 2tan⁻¹ (2x/1 - x²) = π/3

Put x = tanθ

3sin⁻¹ (2tanθ/1 + tan2θ) - 4cos⁻¹ (1 - tan2θ/1 + tan2θ) + 2tan⁻¹ (2tanθ/1 - tan2θ) = π/3

3sin⁻¹ (sin2θ) - 4cos⁻¹ (cos2θ) + 2tan⁻¹ (tan2θ) = π/3

3.2θ - 4.2θ + 2.2θ = π/3

⇒ 2θ = π/3

⇒ θ = π/6

∴ tan-1x = π/6 ⇒ x = tan (π/6) = 1/√3

Thus, The answer is 1/√3

-TheUnknownScientist 72

Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.