Question

plz answer soon................

Answer 1

Answer:

√2-1

Step-by-step explanation:

Given, A + B = 45°

Thus, tan(A + B) = tan 45° = 1

Use the identity

tan(A + B) = $\frac{tan A  + tan B}{1 - tan A tan B}$

or $\frac{tan A  + tan B}{1 - tan A tan B}$ = 1

or tan A + tan B = 1 - tan A tan B

or 1 + tan A + tan B + tan A tan B = 2

or (1 +tan A)(1 + tan B) = 2\

Hence proved.

Now for second part we have to assume A = B

Since A + B = 45°,  A = B = 22.5°

Substituting in the above proved result,

(1 + tan 22.5°)(1  + tan 22.5°) = 2

or (1 + tan 22.5°)² =2

or (1 + tan 22.5°) = √2

or  tan 22.5° =  √2 -1

Hence, value of tan 22.5° is √2-1

I hope this helped u

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