Question

if alpha + beta=90⁰ and alpha= beta÷2 then tan alpha tan beta​

Answer 1

Answer:

The answer is 1.

Step-by-step explanation:

Pls note, that I have used alpha as a and beta as b for my convenience.

Given: a + b = 90⁰ (1)

          And b = 2a

So, solving the equation (1), we have

a + 2a = 90⁰

or, 3a = 90⁰

or, a = 30⁰ and b= 60⁰

Now, tan a = 1/root 3 and tan b = root3

So, we get tan a.tanb = 1(Ans)

Hope it helps u. Have a nice day!

Answer 2

Answer:

1

Step-by-step explanation:

it is given that alpha + beta = 90

=> alpha = 90 - beta --------> Equation 1

but it is given that alpha = beta / 2 --------> Equation 2

LHS of equation 1 and equation 2 are equal

So RHS of equation 1 and equation 2 will be equal

=> 90 - beta = beta / 2

=> 90 = (beta / 2) + beta

=> 90 = (beta / 2) + (beta / 1)

=> 90 = (beta / 2) + (2 beta / 2)

=> 90 = 3 beta / 2

=> 3 beta = 90 * 2

=> 3 beta = 180

=> beta = 180 / 3

= beta = 60°

alpha = 90 - beta

so alpha = 90 - 60

alpha = 30°

tan alpha = tan 30° = 1 / √3

tan beta = tan 60° = √3

so tan alpha * tan beta = (1/√3) * (√3)

= √3 / √3

= 1

So the answer is 1