Question

help............urgently​

Answer 1

Step-by-step explanation:

it is given that, cotx - tanx = m

or, 1/tanx - tanx = m

or, (1 - tan²x)/tanx = m

or, (1 - tan²x)/2tanx = m/2

we know, tan2α = 2tanα/(1-tan²α)

so , (1 - tan²x)/2tanx = 1/tan2x = m/2

or, tan2x = 2/m

from general solution of trigonometric identities.

or, 2x = nπ + tan^-1(2/m)

or, x = nπ/2 + (1/2)tan^-1(2/m)

now a/c to question, we have to find roots in first quadrant.

if m = positive , then n = 0 gives one root of equation.

if m = negative , then n = 1 gives one root of equation.

it means , for a specific situation, given equation has only one roots.

hence, number of roots of equation = 1.

Answer 2

Answer:

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