Question

(sin 30° + tan 45°-
cosec60°)/
(sec 30° + cos 60° - cot 45°)​

Answer 1

Step-by-step explanation:

given that

\frac{(sin30 + tan45 - cosec60)}{(sec30 + cos60 + cot45)}

(sec30+cos60+cot45)

(sin30+tan45−cosec60)

\frac{ \frac{1}{2}+1- \frac{2}{ \sqrt{3}} }{ \frac{2}{ \sqrt{3}}+ \frac{1}{2}+1}

3

2

+

2

1

+1

2

1

+1−

3

2

\frac{ \sqrt{3}+2 \sqrt{3} - 4 }{4 + \sqrt{3} + 2 \sqrt{3} }

4+

3

+2

3

3

+2

3

−4

\frac{ 3 \sqrt{3} - 4 }{4 + 3 \sqrt{3} }

4+3

3

3

3

−4

Rationalise the denominator

\frac{ 3 \sqrt{3} - 4 }{4 + 3 \sqrt{3} } * \frac{ 3 \sqrt{3} - 4 }{3 \sqrt{3} - 4 }

4+3

3

3

3

−4

∗

3

3

−4

3

3

−4

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

(3

3

)

2

−(4)

2

(3

3

−4)

2

\frac{27+16-24 \sqrt{3} }{27-16}

27−16

27+16−24

3

\frac{43-24 \sqrt{3} }{11}

11

43−24

3