Question

Solve cot (π cos θ) = tan (π sin θ).

Answer 1

Answer:

Say π cos θ = B and π sin θ = A. The given equation becomes

cot (B) = tan (A)

or, tan (A) = tan (π/2 – B)

⇒ A = nπ + (π/2 – B)

or, π sin θ = nπ + (π/2 – π cos θ) (sin π + cos π) = n + 1/2.

Divide and multiple by √2 equation reduces to

√2 sin (θ + π/4) = n + 1/2. ……… (1)

Important to remember here is that is it necessary that (n+1/2)/√2 ∈ [–1, 1] i.e. for n = 0, 1/(2√2) ∈ [–1, 1]

for n = 1, 3/2√2 = 3/(2 × 1.414) = 3/2.82 does not belong to [–1, 1]

for n = –1, –1/(2√2) ∈ [–1, 1]

Hence (1) becomes

sin (θ + π /4) = +1/2√2

⇒ θ = kπ + (–1)k (± sin–11/2√2) – π /4

θ = kπ + (–1)k sin–1(1/2√2) – π /4, where n = 0, ±1, ±2 …

Hope it helps

Answer 2

Answer:

have behind nonsenses

Step-by-step explanation:

pi theta cos theta