Question

(TanX-1)(CosX-1)=0.

Answer 1

Given trigonometric equation is ( Tan x - 1 ) ( cos x - 1 ) = 0.

Apply zero property .

( Tan x - 1 )  = 0  or   ( cos x - 1 ) = 0.

Tan x   = 1 or   cos x = 1

Tan x   = 1 or  cos x = 1

Solution :

Comments

• tan x = 1.

tan x = tan π /4.

The genaral solution of tan(θ) = tan(α) is θ = nπ + α, where n is an integer.

⇒ x = nπ + π /4.

• cos (x) = 1.

cos (x) = cos(0)

The genaral solution of cos(θ) = cos(α) is θ = 2nπ ± α, where n is an integer.

⇒x = 2nπ ± (0)

x = 2nπ.

The solutions are x = nπ + π /4 and x = 2nπ, where n is an integer.

Answer 2

Given trigonometric equation is ( Tan x - 1 ) ( cos x - 1 ) = 0.

Apply zero property .

( Tan x - 1 )  = 0  or   ( cos x - 1 ) = 0.

Tan x   = 1 or   cos x = 1

The equation is Tan x = 1 -----> .

The function Tan x has period of , first find all solutions in the interval .

The function Tan x is positive in first and third quadrant.

In first quadrant,

.

In third quadrant,

So the solutions are .

Finally, add multiples of to each of these solutions to get the general form

where n is integer.

The equation is cos x = 1 -------->

The function has a period of , first find all solutions in the interval .

The function cos x is positive in first and fourth quadrant.

In first quadrant,

.

Finally, add multiples of to each of these solutions to get the general form where n is integer.

The solutions are .

 

Comments

• tan x = 1.

tan x = tan π /4.

The genaral solution of tan(θ) = tan(α) is θ = nπ + α, where n is an integer.

⇒ x = nπ + π /4.

• cos (x) = 1.

cos (x) = cos(0)

The genaral solution of cos(θ) = cos(α) is θ = 2nπ ± α, where n is an integer.

⇒x = 2nπ ± (0)

x = 2nπ.

The solutions are x = nπ + π /4 and x = 2nπ, where n is an integer.