Question

Solve the equation cot⁡ x + tan⁡ x =2cosecx​

Answer 1

Answer:

cot x + tan x can be simplified as

2cosec2x

this can be done by replacing

cot by cosx/sinx and tan by sinx/cosx

so we get

2cosec2x=2cosec x

so

cosec2x=cosec x

or

sin2x=sinx

sin 2x=2sinx×cosx

so

sin2x = sin x

can be written as

2sinx×cosx = sin x

sin x gets cancelled so

Sin x = 0 will be a solution

and remaining

cosx=1/2

will be a solution

npi and 2npi +- 60 will be a solution

Answer 2

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