Question

√3sinQ=cosQ find the value of sin Q(tanQ)(1+cotQ)/(sinQ+cosQ)
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Answer 1

Answer:

$\frac{ \sqrt{3} (2 + \sqrt{3} )}{2}$

Step-by-step explanation:

Given that

$\sqrt{3} sin \alpha = cos \alpha \\ => \frac{sin \alpha }{cos \alpha } = \sqrt{3} \\ => tan \alpha = \sqrt{3} \: \: \\ \: \: => tan \alpha = tan {60}^{0} \\ => \alpha = {60}^{0}$

Now the given expressions is

$sin \alpha tan \alpha (1 + cot \alpha )(sin \alpha + cos \alpha )$

$= \frac{ \sqrt{3} }{2} \times \sqrt{3} (1 + \frac{1}{ \sqrt{3} } )( \frac{ \sqrt{3} }{2} + \frac{1}{2} )$

$= \frac{3}{2} ( \frac{ \sqrt{3} + 1}{ \sqrt{3} } )( \frac{ \sqrt{3} + 1}{2} )$

$= \frac{3 {( \sqrt{3} + 1)}^{2} }{4 \sqrt{3} }$

$= \frac{ \sqrt{3} (3 + 2 \sqrt{3 } + 1)}{4}$

$= \frac{ \sqrt{3} (4 + 2 \sqrt{3} )}{4}$

$= \frac{2 \sqrt{3}(2 + \sqrt{3} ) }{4}$

$= \frac{ \sqrt{3}(2 + \sqrt{3})}{2}$