Question

Simplity 1-tan 45º tan 30°
Simplify tan 45º + tan 30°​

Answer 1

Answer:

1. 1 - tan 45° tan 30°

$1 - 1 \times \frac{1}{\sqrt{3}}$

[since tan 45° = 1 and tan 30° = 1/√3]

$0 \times \frac{1}{\sqrt{3}}$

1 - tan 45° tan 30° = 0

2. tan 45° + tan 30°

$1 + \frac{1}{\sqrt{3}}$

[since tan 45° = 1 and tan 30° = 1/√3]

$\frac{\sqrt{3} + 1}{\sqrt{3}}$

$\frac{\sqrt{3} + 1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

[Rationalising the denominator]

$\frac{3 + \sqrt{3}}{3}$

$\bold{\therefore \frac{3 + \sqrt{3}}{3}}$

$\Large{\bold{\boxed{\underline{\red{\mathfrak{Note:}}}}}}$

Avoid writing square roots in the denominators. If possible, rationalise them.

Answer 2

∆. 1-tan45 tan30

$1 - tan45 \: tan30 \\ \\ = 1 - (1)( \frac{1}{ \sqrt{3} } ) \\ \\ = 1 - \frac{1}{ \sqrt{3} } \\ \\ = \frac{ \sqrt{3} - 1}{ \sqrt{3} } \\ \\or \\ \\ = \frac{ \sqrt{3} - 1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{3 - \sqrt{3} }{3}$

∆. tan45 + tan30

$tan45 + tan30 \\ \\ = 1 + \frac{1}{ \sqrt{3} } \\ \\ = \frac{ \sqrt{3} + 1 }{ \sqrt{3} } \\ \\ or \\ \\ \frac{ \sqrt{3} + 1 }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{3 + \sqrt{3} }{3}$

hope it helps you..........

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