Question

Prove that

$\sf (1+tan15)(1+tan30)=2$​

Answer 1

To Prove:

___________

$\sf (1+tan15)(1+tan30)=2$

Given that, we have to prove:

________________________________

(1 + tan\ 15)(1 + tan\ 30) = 2(1+tan 15)(1+tan 30)=2

From trignometric ratios, we know that,

tan 30° = 1/√3 =0.577350

tan 15° = 2 - √3 = 0.267949

Therefore, plug in these values in left

hand side of given equation

Substituting the values we get,

\begin{gathered}(1 + 0.267949)(1+0.577350) = 1.267949 \times 1.577350 \\\\(1 + 0.267949)(1+0.577350)=1.9999 \approx 2\end{gathered}

(1+0.267949)(1+0.577350)=1.267949×1.577350

(1+0.267949)(1+0.577350)=1.9999≈2

Thus (1 + tan15)(1 + tan30) = 2 is proved

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