Lf the tan A +cosA=2find the value of cosA

Step-by-step explanation:

Given :

tan A + cot A = 2,

Then, cos A = ?

Solution :

We know that,

cot A=\frac{1}{tan A}cotA=

tanA

1

So,

tan A + cot A = 2,

⇒ tan A + \frac{1}{tan A} = 2tanA+

tanA

1

=2

⇒ \frac{tan^2A+1}{tanA} = 2

tanA

tan

2

A+1

=2

⇒ tan^2A + 1 = 2 tanAtan

2

A+1=2tanA

⇒ tan^2A - 2 tanA+1=0tan

2

A−2tanA+1=0

⇒ tan^2A - tan A - tan A+1 = 0tan

2

A−tanA−tanA+1=0

⇒ tanA(tanA-1)-1(tanA-1)=0tanA(tanA−1)−1(tanA−1)=0

⇒ (tanA-1)^2=0(tanA−1)

2

=0

Taking square root both the sides,.

⇒ tanA-1=0tanA−1=0

⇒ tanA = 1tanA=1

⇒ tanA=tan45tanA=tan45 °

So,

⇒ A=45A=45 °

Hence,

cosA=cos45cosA=cos45 ° =\frac{1}\sqrt{2}}

⇒ cosA =\frac{1}\sqrt{2}}

its adding 5.5 each time

step-by-step explanation: