Question

if A+B=45°than show that (1+tanA)(1+tanB)=2 explain in telugu<br /><br /><br />​

Answer 1

Answer:

It's a proof.. to prove the validity of an equation.

Step-by-step explanation:

A+B=45°.

so Tan(A+B) = 1

so (Tan A + Tan B )/(1-Tan A ×Tan B) = 1.

Take the denominator to the other side and rearrange the factor on the RHS.

so Tan A + Tan B + Tan A × Tan B = 1

Add 1 on both sides and factorize the LHS to get

(1+Tan A) (1+Tan B) = 2.

proved.

done.

Answer 2

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

Given that,

$\sf{x + y = 45} \\ \\ \longrightarrow \: \sf{tan(x + y) = tan 45}$

To Prove

$\sf (1 + tan \: x)(1 + tan \: y) = 2$

Now,

$\longrightarrow \: \sf{ \dfrac{tan \: x + tan \: y}{1 - tan \: x.tan \: y} = 1 } \\ \\ \longrightarrow \: \sf{tan \: x + tan \: y = 1 - tan \: x.tan \: y} \\ \\ \longrightarrow \: \underline{\boxed{\sf{tan \: x + \: tan \: y + tan \: x.tan \: y = 1}}}$

Adding one on both sides,we get :

$\longrightarrow \: \sf{tan \: x + tan \: y + tan \: x.tan \: y + 1 = 1 + 1} \\ \\ \longrightarrow \: \sf{1(1 + tan \: x) + tan \: y(1 + tan \: x) = 2} \\ \\ \longrightarrow \: \tt{(1 + tan \: x)(1 + tan \: y) = 2}$

Henceforth,Proved