Question

[sin30°+ tan 45°- cosec60°]/sec30°+cos60°+cot45°
what is the answer????​

Answer 1

Step-by-step explanation:

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Answer 2

$\frac{( \sin(30) + \tan(45) - \cosec(60) }{( \sec(30) + \cos(60) + \cot(45)) }$

$= > \frac{ \frac{1}{2} + 1 - \frac{2}{ \sqrt{3} } }{ \frac{2}{ \sqrt{3} } + \frac{1}{2} + 1 }$

$= > \frac{ \sqrt{3} + 2 \sqrt{3} - 4 }{4 + \sqrt{3} + 2 \sqrt{3} }$

$= > \frac{ 3\sqrt{3} - 4 }{4 + 3 \sqrt{3} }$

Rationalising the denominator

$= > \frac{ 3\sqrt{3} - 4 }{4 + 3 \sqrt{3} } \times \frac{ 3\sqrt{3} - 4 }{3 \sqrt{3} - 4 }$

$= > \frac{ {(3 \sqrt{3} - 4) }^{2} }{ {(3 \sqrt{3 }) }^{2} - {(4)}^{2} }$

$= > \frac{27 + 16 - 24 \sqrt{3} }{27 - 16}$

$= > \frac{43 - 24 \sqrt{3} }{11}$