Question Bank - Mathematics

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If tan ? + tan ? = 1 - tan ?.tan ?, where tan ? tan ? ? 1, then which of the following is one of the values of (? + ?) ?

A.
\(\frac{\pi}{6}\)
B.
\(\frac{\pi}{4}\)
C.
\(\frac{\pi}{3}\)
D.
\(\frac{\pi}{2}\)

Solution:

Formula used:tan(A + B) = \(\frac{tan \ A + tan\ B }{1-tan\ A\ tan\ B}\)Calculation:Given that,tan ? + tan ? = 1 - tan ?.tan ? -----(1)By using the above formula, we can writetan(? + ?) = \(\frac{tan \ ? + tan\ ? }{1-tan\ ?\ tan\ ?}\)? tan(? + ?)(1 - tan? tan ?) = tan ? + tan? Using equation (1)? tan(? + ?) (tan ? + tan ?) = (tan ? + tan?) ? tan(? + ?) = 1? (? + ?) = \(\frac{\pi}{4}\)? The values of (? + ?) is \(\frac{\pi}{4}\).

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