Question

Let f(x) = sinx.cos³x and g(x) = cosx.sin³x, then the value of `7((f(π/7) + g(π/7))/(g((5π)/14) + f((5π)/14)))` is ______.

विकल्प

• 5.00

• 6.00

• 7.00

• 8.00

Answer 1

Let f(x) = sinx.cos³x and g(x) = cosx.sin³x, then the value of `7((f(π/7) + g(π/7))/(g((5π)/14) + f((5π)/14)))` is 7.00.

Explanation:

Use `π/7 + (5π)/14 = π/2` and `sin(π/2 - θ)` = cosθ

We know f(x) + g(x) = sinxcosx(cos²x + sin²x)

= sinxcosx

`f(π/7) + g(π/7) = sin  π/7. cos  π/7`

= `sin(π/2 - (5π)/14) cos(π/2 - (5π)/14)`

= `cos  (5π)/14 sin  (5π)/14`

= `g((5π)/14) + f((5π)/14)`

Now, `7[(f(π/7) + g(π/7))/(g((5π)/14) + f((5π)/14))]` = 7